Question

An isosceles right triangle has area $8{\text{cm}}^2$. The length of hypotenuse is

• A. $\sqrt{48}$ cm
• B. $\sqrt{16}$ cm
• C. $\sqrt{24}$ cm
• D. $\sqrt{32}$ cm

Answer 1

The correct option is D $\sqrt{32}$ cm

Step 1: Find the length of equal sides​

Given : Area of isosceles right triangle $=8{\text{cm}}^2$

Let the height of triangle $=h\text{cm}$

As the triangle is isosceles,

$\therefore$ Base $=$ Height $=h\text{cm}$

Area of triangle $=\frac{1}{2}\times \text{Base}\times \text{height}$

$\Rightarrow 8=\frac{1}{2}\times h\times h$

$\Rightarrow 16=h^2$
$\Rightarrow h=4\text{cm}(\therefore h\text{cannot be negative})$

Thus, Base $=$ Height $=4\text{cm}$

Step 2: Find the length of hypotenuse​

​Since the triangle is right angled,

By Pythagoras theorem,

${\text{Hypotenuse}}^2={\text{Base}}^2+{\text{Height}}^2$

$\Rightarrow \text{Hypotenuse}=\sqrt{{\text{Base}}^2+{\text{Height}}^2}$

$=\sqrt{4^2+4^2}$

$=\sqrt{16+16}$

$=\sqrt{32}$

Thus, the length of the hypotenuse is $\sqrt{32}$ cm.

Hence, (a) is the correct answer.