The area of an isosceles right angled triangle is 121 cm² . Find its hypotenuse

22 cm

Area of triangle = \(\frac{1}{2}\)× base × height

According to Pythagoreans theorem

(Hypotenuse)² = (Perpendicular)² + (Base)²

Let the base and height of the isosceles triangle be ‘x’

Area of triangle = \(\frac{1}{2}\)× base × height

= 121 = \(\frac{1}{2}\)× x × x

= x² = 242

= x = √242 = 11√2

We know that,

(AC)² = (AB)² + (BC)²

= (AC)² = (11√2)² + (11√2)²

= (AC)² = 242 + 242

= (AC)² = 484

= AC = √484 = 22 cm