What is the area of the following parallelogram in square centimeters?
A) 396 cm2
B) 360 cm2
C) 3.6 cm2
D) 3.96 cm2
Which of the following sets of numbers is a Pythagorean triple?
A) 42, 40, 82
B) 42, 40, 58
C) 41, 41, 58
D) 40, 41, 57
Answers
Answer with explanation:
1.⇒Area of Parallelogram = Corresponding height × Base
= 2 cm × 18 mm
→1 cm = 10 mm
So, Area of Parallelogram
= 2 cm × 1.8 cm
= 3.6 cm²
Option C: →3.6 cm²
→→→2. A triplet ,that is set of three numbers is called Pythagorean triplet, if it is of the form of : {m²-1, 2 m , m²+1}
That is if you write the Pythagorean rule for Right triangle, having sides , m²-1, 2 m , m²+1
then ,→ Square of Largest side = Sum of squares of two smallest side
Square of Largest Side = (m²+1)²
Sum of squares of two smallest side= (2 m)² + (m²-1)²
= 4 m² + (m²)² -2 m²+1
= (m²)² +2 m²+1
=(m²+1)²
So, we will check out , out of four options which of them are Pythagorean Triplet.
Option 1.
Square of Largest Number = 82²=6724
Sum of squares of two smaller number= 42² + 40²
= 1764 +1600
= 3364
→Square of Largest Number ≠Sum of squares of two smaller number
6724 ≠ 3364
Not a Pythagorean Triple.
Option 2.
Square of Largest Number = 58²=3364
Sum of squares of two smaller number= 42² + 40²
= 1764 +1600
= 3364
→Square of Largest Number =Sum of squares of two smaller number
3364= 3364
A Pythagorean Triple.
Option 3.
Square of Largest Number = 58²=3364
Sum of squares of two smaller number= 41² + 41²
= 1681 +1681
= 3362
→Square of Largest Number ≠Sum of squares of two smaller number
3364 ≠ 3362
Not a Pythagorean Triple.
Option 4.
Square of Largest Number = 57²=3249
Sum of squares of two smaller number= 41² + 40²
= 1681 +1600
= 3281
→Square of Largest Number ≠Sum of squares of two smaller number
3249 ≠ 3281
Not a Pythagorean Triple.
Option B: (42, 40,58) is a Pythagorean triple.
Answer:
C
Step-by-step explanation:
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