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The area of isosceles right angle triangle is 72 cm2. Find the area of the square whose side is equal to hypotenuse of isosceles right angle triangle.

The area of isosceles right angle triangle is 72 cm2. Find the area of the square whose side is equal to hypotenuse of isosceles right angle triangle. Correct Answer 288 cm<sup>2</sup>

Given: 

The area of the isosceles right-angle triangle is 72 cm2

The side of the square is equal to the hypotenuse of isosceles right angle triangle

Concept: 

Area of isosceles right-angle triangle = 1/2 × (Product of equal side) 

H2 = P2 + B2

Area of the square = Side2

Calculation: 

Let the equal side of the triangle is b cm

The area of the triangle is 

⇒ 1/2 × b × b = 72 

⇒ b2 = 144 

⇒ b = 12

The equal side of the triangle is 12 cm

Now, 

H2 = 122 + 122

⇒ H = (2 × 144)1/2

⇒ H = 12√2 cm

Here, the Side of the square is also 12√2 cm

So, 

The area of the square is 

⇒ (12√2)2 

⇒ 144 × 2

⇒ 288 cm2

∴ The required area of the square is 288 cm2.

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