The triangles below are similar. The ratio of the lengths of corresponding sides is 49 . a. What is the ratio (smaller to larger) of the perimeters? b. What is the ratio (smaller to larger) of the areas? The image is of two similar triangles with proportionate side of each marked as 4 in. and 9 in. respectively.
Answers
Answer:
a.) 4 : 9
b.) 16 : 81
Explanation:
a.) Ratio of perimeter will still be
4 : 9
b.) The two similar triangles ΔABC and ΔDEF as shown from the attached figures. That is
AB/DE = AC/DF = BC/EF
It is apparent that ΔAPB and ΔDEQ are also similar as all respective angles are equal. Hence,
AB/DE = AP/DQ = BP/EQ
Moreso ΔABC = 1/2 × BC × AP and ΔDEF = 1/2 × EF × DQ and
ΔAPB/ΔDEQ = BC/EF × AP/DQ
But
AP/DQ = AB/DE = BC/EF
and hence
ΔAPB/ΔDEQ = BC/EF × BC/EF
= BC^2/EF^2 and as
BC/EF = AC/DF = AB/DE
ΔAPB/ΔDEQ = AC^2/DF^2 = BC^2/EF^2
= AB^2/DE^2
Hence if sides of two similar triangles are in the ratio a:b, their areas are in the proportion a^2:b^2
As in given case sides are in the ratio of 4:9.
ratio of their areas is 4^2:9^2 or 16:81.
The ratio (smaller to larger) of the perimeters of this similar triangle is equal to 4:9 and 16:81 for their areas.
Given the following data:
Ratio = 4:9Side length of smaller triangle = 4 inches.Side length of larger triangle = 9 inches.What is a triangle?A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
How to calculate the perimeter of a triangle.Mathematically, the perimeter of a triangle is given by this formula:
[tex]P=A+B+C[/tex]
Where:
A, B, and C are length of sides.What is scale factor?Scale factor can be defined as the ratio of two (2) corresponding length of sides in two similar geometric figures such as equilateral triangles.
In Geometry, if the scale factor of two (2) similar geometric figures is given as a:b, then;
The ratio of their perimeters is equal to a:b.The ratio of their areas is equal to [tex]a^2:b^2[/tex].In conclusion, the ratio (smaller to larger) of the perimeters of this similar triangle is equal to 4:9. Also, the ratio (smaller to larger) of their areas is equal to [tex]4^2 :9^2=[/tex] 16:81.
Read more on perimeter of a triangle here: https://brainly.com/question/24382052
Related Questions
If a recipe for chocolate chip cookies uses 5 cups of chocolate chips for 3 batches, how many cups of chocolate chips are needed for 5 batches? (Round your answer to the nearest tenth of a cup.
Answers
Answer:
5 cups of chocolate chips for 3 batches, then
x cups of chocolate chips for 5 batches.
x/5 = 5/3
=> x = 5 x 5/3 = 25/3 = 8.3
Hope this helps!
:)
Answer:
8.3
Explanation:
X=25/3
X=8/3
Will give brainliest! please answer!
Answers
A ____ is used to apply for jobs or even to college.
A. cover letter
B. work history report
C. job description
D. résumé
Answers
A resume is used to apply for jobs or even to college.
What is Resume?
The secret to producing a résumé that stands out is preparation. You will save time and ensure that you present your best self if you have your crucial facts prepared. These are some helpful resume writing tips.
While crafting a strong CV, you must analyze your relevant experience and match it to the demands of the position you're applying for.
Before you can start writing a resume, you must first format one. Three forms are accepted as standards. Choose the resume format that best suits your level of work experience and your career objectives by using the same elements of a resume but organizing them differently.
Therefore, A resume is used to apply for jobs or even to college.
To learn more about Resume, refer to the link:
https://brainly.com/question/862477
#SPJ7
In the last hour, Ellie observed 32 monarchs, 56 gulf fritillaries, and 8 giant swallowtails visit her butterfly garden. If 480 butterflies visit her garden, how many can we expect will be giant swallowtails?
Answers
Answer:
40 is the answer
Explanation:
As per the given details, we can expect that 40 of the 480 butterflies that visit Ellie's garden will be giant swallowtails.
What is fraction?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator.
Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.
The total number of butterflies observed in the last hour is:
32 + 56 + 8 = 96
This represents the fraction of the total butterflies that were observed, and we can set up a proportion to solve for the number of giant swallowtails in the total population:
8/96 = x/480
Multiplying both sides by 480, we get:
x = (8/96) * 480
x = 40
Therefore, we can expect that 40 of the 480 butterflies that visit Ellie's garden will be giant swallowtails.
For more details regarding fraction, visit:
https://brainly.com/question/10354322
#SPJ7
8 yd
10 yd
y3 yd
Find the volume of the triangular prism
A 120 yd
B. 130 yd
C. 240 yd
D. 260 yd
Answers
Twenty is 7 less than twice the number w. What is the value of w?
Answers
Answer:
13.5
Explanation:
To find 2w, we add 20+7=27 to get 27=2w, then we go and divide both sides by 2 to get our answer 13.5
Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. What is Aaron’s total charge, in dollars, for staying 3 nights?
Answers
Answer:
The total charge of Aaron after 3 nights:
C = 99.95 x (1 + 8/100) x 3 + 5 = 328.84 dollar
Hope this helps!
:)
Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. Aaron’s total charge, in dollars, for staying 3 nights is 328.84 dollars.
What is the charge?Charge or payment is a given amount of money on which, in exchange, we get to use things or buy things. Hotels, restaurants, and café are the places that charge you money in exchange for using their resources.
Given, the hotel charges $99.95 per night
The tax applied is 8% for the room rate
An additional one-time charge is $5.00
The total charge in dollars is:
The total charge of Aaron after 3 nights:
C = $99.95 x (1 + 8 / 100) x 3 + $5 = 328.84 dollar
As, 8%, so 8 will be divided by 100 and all others are money in dollars.
Therefore, the total charge to Aaron after 3 nights is $328.84.
To learn more about charge, refer to the link:
https://brainly.com/question/16916769
#SPJ2
Select all of the measurements that are equivalent to 528 meters.
A. 52,800 cm
B. 528,000 km
C. 5,280 cm
D. 528,000 mm
E. 0.528 km
Answers
Explanation:
[tex]528m = 52800cm \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.528km[/tex]
Will give brainliest! please answer correctly!
Answers
Answer:
B
Explanation:
Answer:
C. There is no solution
Explanation:
brainliest?
Calculate the speed of the 0.66 kg ball just before the collision.
Calculate the speed of the 0.22 kg ball immediately after the collision.
Calculate the speed of the 0.66 kg ball immediately after the collision.
Indicate the direction of motion of the 0.66 kg ball immediately after the collision.
____ To the left ____ To the right
Calculate the height to which the 0.66 kg ball rises after the collision.
Based on your data, is the collision elastic?
____ Yes ____ No
Justify your answer.
Answers
Answer:
The experimental apparatus shown in the figure above contains a pendulum consisting of a 0.66 kg ball attached
to a string of length 0.60 m. The pendulum is released from rest at an angle of 60 degrees and collides with a ball of mass 0.22 kg initially at rest at the edge of a table. The 0.22 kg ball hits the floor a distance of 1.4 m from the
edge of the table.
(a) Calculate the speed of the 0.66 kg ball just before the collision.
2.4 m/s
(b) Calculate the speed of the 0.22 kg ball immediately after the collision.
2.8/m s
(c) Calculate the speed of the 0.66 kg ball immediately after the collision.
1.5 m/s
(d) Indicate the direction of motion of the 0.66 kg ball immediately after the collision.
____ To the left __X__ To the right
(e) Calculate the height to which the 0.66 kg ball rises after the collision.
0.11 m
(f) Based on your data, is the collision elastic?
____ Yes __X__ No
Coefficient of elasticity of less than one means an inelastic collision.
Justify your answer.
Explanation:
See attached.
how much work can be done with 10 joules of energy? fast plsssss
Answers
Answer:
10J of work
Explanation:
C=59(F−32)The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59degree Celsius. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answers
Answer:
D
Explanation:
Our answer choices are:
- A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degrees Celsius.
- A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
- A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
Let's try the first one. We can just choose any temperature and then use the number 1 larger than it; let's do F = 10:
C = (5/9) * (10 - 32) = (5/9) * (-22) ≈ -12.2
When F = 10 + 1 = 11:
C = (5/9) * (11 - 32) = (5/9) * (-21) ≈ -11.7
We see that indeed, -11.7 - (-12.2) ≈ 0.56 ≈ 5/9, so the first is correct.
For the second, let's see what happens when C = 10 and when C = 11:
10 = (5/9) * (F - 32)
F = 50
11 = (5/9) * (F - 32)
F = 51.8
Again we see that indeed 51.8 - 50 = 1.8
So, the second choice is also correct.
Thus, the answer is D.
Answer:
D
Explanation:
C = 5/9(Fahrenheit - 32)
C = 5/9Farenheit - 160/9
F = 9C/5 + 32
As Fahrenheit increases by 1, C increases by 5/9.
As C increases by 1, Fahrenheit increases by 9/5 (1.8)
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9degree Celsius. (True)
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. (True)
A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. (False)
Will give brainliest! please answer correctly!
Answers
If explanation is needed let me know
It is A and C
Explanation:
Bella is making button barrettes. She allows each of her friends to reach into her bag of buttons and randomly select a color. Then she replaces it with the same color button and shakes the bag before letting another friend pick a color. Bella's bag of buttons contains the colors below. Which model shows the probability of randomly selecting each color button from her bag? If 50 her friends choose a button from the bag, about how many pink barrettes can she expect make?
Answers
Answer: 6
Explanation:
As per the given data, if 50 her friends choose a button from the bag, she can expect to make 6 pink barrettes.
What is probability?Probability is simply the likelihood of something occurring. When we are uncertain about the outcome of an event, we can discuss the probabilities of various outcomes—how likely they are. Statistics is the study of events governed by probability.
It is based on the likelihood of something occurring. The reasoning behind probability is the foundation of theoretical probability. If a coin is tossed, the theoretical probability of getting a head is 1/2.
Here, it is given that,
Total no. of buttons = 300 + 700 + 1000 + 500 = 2500
probability for a person to pick a pink button = 300/2500 = (3/25)%
Number of pink buttons she can expect her friends to pick = 50(3/25) = 6
Thus, the answer is 6.
For more details regarding probability, visit:
https://brainly.com/question/30034780
#SPJ7
Which of the following is considered to be typical information needed on a
job application?
A. Misdemeanor convictions
B. Student ID number
C. Felony convictions
D. GPA
Answers
Answer: felony convictions
Explanation:
Which sentence best uses the active voice to emphasize the actions of the subject? A. Finn's science project was appreciated by his teacher. B. Jared's performance was recorded by the local news station. C. Ross ate his sandwich after completing his work. D. The stage curtains were drawn before the play.
Answers
Answer:
d
Explanation:
Answer:
C. Ross ate his sandwich after completing his work.
Explanation:
In sentences written in active voice, the subject performs the action expressed in the verb. In this case, Ross, the subject, performs the action of eating. Therefore, the correct answer is "Ross ate his sandwich after completing his work."
It was a study island question.
Nine less than twice x is three more than x. What is the value of x?
Answers
2x -9 = x + 3
-x -x
x -9 = 3
+9 +9
x = 12
What is the distinguishing feature of a coronavirus
Answers
Answer:
The common cold, though rarer forms can be lethal, such as SARS, MERS.
Explanation:
Which of the following was a lasting effect on Europe as a result of the Crusades?
A. Europe became more isolated
B.
Trade between Europe and the East increased
C. Many Europeans converted to Islam
D.
Many Muslims moved to Europe,
Reset
Submit
Answers
Answer:
the answer is d because i said so
Explanation:
I do not get what you ask for??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Answers
Answer:?
Explanation: Me neither
a particular car has a fuel efficiency for 8 liters of gasoline per 100 kilometers. What is the fuel efficiency in miles per gallon?
Answers
To convert a car's fuel efficiency from 8 liters per 100 kilometers to miles per gallon, first convert kilometers to miles and liters to gallons, then divide the miles by the gallons to get approximately 29.4 MPG.
Explanation:A student asked about converting a car's fuel efficiency from 8 liters of gasoline per 100 kilometers to miles per gallon (MPG). To do this conversion, we need to use the following conversions: 1 kilometer = 0.621371 miles, 1 liter = 0.264172 gallons. Thus, 8 liters per 100 kilometers translates to essentially how many miles you can travel on 0.264172 gallons per 62.1371 miles.
First, convert 100 kilometers to miles: 100 kilometers * 0.621371 = 62.1371 miles. Next, convert 8 liters to gallons: 8 liters * 0.264172 = 2.113376 gallons. Finally, to find the MPG, divide the miles by the gallons: 62.1371 miles / 2.113376 gallons ≈ 29.4 MPG.
This calculation demonstrates the fuel efficiency of the car in terms familiar to those using the imperial system, helpful for comparing vehicle efficiency in regions that use MPG as a standard measurement.
QUESTION 8
Which of the following statements about taxes is FALSE?
Taxes are collected at the local, state and federal level
Some states don't collect income tax
Some states don't collect sales tas
Taxes at the local, state and federal level are all equal
Answers
Answer:
FALSE: Taxes at the local, state and federal level are all equal.
Explanation:
Taxes at the local, state, and federal level are all equal is FALSE.
Taxes are indeed collected at the local, state, and federal levels, so this statement is true.Some states, like Florida and Texas, do not collect a state income tax, so this statement is true.Some states, such as Delaware and Montana, do not have a state sales tax, so this statement is true.However, taxes at the local, state, and federal levels are not equal in amount or purpose; they vary greatly depending on jurisdiction and tax type.A piece of land was purchased for $65,000. The value of the land has slowly been decreasing by 1% annually. How much will the land be worth in 20 years?
Answers
Explained how to calculate the decreased value of land after 20 years with an annual 1% decrease.
Explanation:The land value after 20 years:
To calculate the value of the land after 20 years with a 1% annual decrease, you can use the formula:
V = $65,000 x (1 - 0.01)^20
After 20 years, the land will be worth approximately $43,206.08.
the large rectangle below represents one whole