Question

An isosceles right triangle has area $8c{m}^2$. The length of its hypotenuse is

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

Answer 1

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

Explanation:

Let height of triangle = $h$

As the triangle is isosceles,

Let base = height =$h$

According to the question, Area of triangle = $8c{m}^2$

$⟹\frac{1}{2}\times Base\times Height=8$

$⟹\frac{1}{2}\times h\times h=8$

$⟹h^2=16$

$⟹h=4cm$

Base = Height = $4cm$

Since the triangle is right angled,

$Hypotenus{e}^2=Bas{e}^2+Heigh{t}^2$

$⟹Hypotenus{e}^2=4^2+4^2$

$⟹Hypotenus{e}^2=32$

$⟹Hypotenuse=\sqrt{32}$

Hence, Options $A$ is the correct answer.