Question

If an isosceles right triangle has area $8c{m}^2,$ then the length of its hypotenuse is

• A. $\sqrt{24}cm$
• B. $4cm$
• C. $\sqrt{32}cm$
• D. $\sqrt{48}cm$

Answer 1

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

Given: Area of an isosceles right triangle $=8c{m}^2$

As the triangle is isosceles,

Let base$=$ height $=h$

$\Rightarrow \frac{1}{2}\times \text{base}\times \text{height}=8$

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

$\Rightarrow h^2=16$

$\Rightarrow h=4cm$

$\therefore$ Base$=$ Height $=4cm$

Since the triangle is right angled,

$(hypotenuse{)}^2=(base{)}^2+(height{)}^2$

$\Rightarrow (hypotenuse{)}^2=(4{)}^2+(4{)}^2$

$\Rightarrow (hypotenus{)}^2=16+16$

$\Rightarrow (hypotenuse{)}^2=32$

$\Rightarrow \text{hypotenuse}=\sqrt{32}cm$

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

Hence, $\left(a\right)$ is the correct answer.