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If the area of an isosceles right triangle and a square are same, then, find the ratio between the hypotenuse of the triangle and the diagonal of the square?

If the area of an isosceles right triangle and a square are same, then, find the ratio between the hypotenuse of the triangle and the diagonal of the square? Correct Answer √2 : 1

Given:

Area of isosceles right triangle = Area of square

Formula used:

Area of square = (side)2

Area of isosceles right triangle = ½ × (side)2

Calculation:

Suppose the side of an isosceles right triangle is a cm and the side of a square is b cm.

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According to question –

Area of isosceles right triangle = Area of square

⇒ ½ × a × a = b × b

⇒ a = b√2

According to question-

∴ Required ratio = (a√2)/(b√2) = (b√2 × √2)/(b√2) = √2 : 1

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