The area of an isosceles right angled triangle is 121 cm$$^2$$. Find its hypotenuse.

Let the base and height of the isosceles right angled triangle = $$a$$

Area of the triangle = $$\frac{1}{2}\times$$ base $$\times$$ height = $$\frac{1}{2}\times a\times a$$ = $$\frac{1}{2}a^2$$

Given, area of the triangle = 121 cm$$^2$$

$$\Rightarrow$$  $$\frac{1}{2}a^2=121$$

$$\Rightarrow$$  $$a=11\sqrt{2}$$

In the isosceles right angled triangle,

Hypotenuse$$^2$$ = $$a^2+a^2$$

$$\Rightarrow$$  Hypotenuse$$^2$$ =  $$2a^2$$

$$\Rightarrow$$  Hypotenuse$$^2$$ = $$2\left(11\sqrt{2}\right)^2$$

$$\Rightarrow$$  Hypotenuse$$^2$$ = $$121\times4$$

$$\Rightarrow$$  Hypotenuse = 22 cm

Hence, the correct answer is Option C