Question

Find the length of the hypotenuse of an isosceles
right triangle with area 722

Answer 1

Answer:

38√2 unit     or  53.73 unit

Step-by-step explanation:

In isosceles triangle, two sides are equal. In isosceles right triangle, sides other than hypotenuse are equal.

 Let the length of each equal side be 'x'.

⇒ x² + x² = hypotenuse²

⇒ 2x² = hypotenuse²        ...(1)

  Given,  area of this triangle is 722 unit^2.

⇒ Area = 1/2 * height * base

⇒ 722 = 1/2 * x * x

⇒ 1444 = x²

Substitute the value of x² in (1)

        ⇒ 2(1444) = hypotenuse²

        ⇒ 2888 = hypotenuse

        ⇒ √2888 = hypotenuse

        ⇒ 38√2

Taking √2 = 1.414,  hypotenuse = 53.73 unit

Answer 2

For the explanations Refer the above attachments .