If the area of a right-angled isosceles triangle is 676 cm² , then the length of its hypotenuse is:

52 cm

We know that,

Area of right angled isosceles triangle = \(\frac{1}{2}\) × a × a

a = equal sides of triangle

Given,

Area of right angled isosceles triangle = 676 sq.cm

Let height or base of right angled triangle be x cm.

= 676 = \(\frac{1}{2}\) × x²

= a = 26\(\sqrt {2}\) cm

Height and base of isosceles triangle = 26\(\sqrt {2}\) cm

In right angled triangle,

Using pythagoras theorem,

hypotenuse² = a² + a²

hypotenuse² = 2a²

hypotenuse = \(\sqrt {2}\) × a

hypotenuse = \(\sqrt {2}\) × 26\(\sqrt {2}\) = 26 × 2 = 52