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 for the correct option:

Find the equal sides of the isosceles right-angled triangle

Let the equal sides (base and height) of the triangle be $acm$.

We know that the area of the triangle $=\frac{1}{2}\times base\times height$

Since it is given that the area of the isosceles right triangle is $8c{m}^2$.

Now,

$$\begin{gathered} \frac{1}{2}\times a\times a=8 \\ \Rightarrow a^2=16 \\ \Rightarrow a=4cm \end{gathered}$$

Find the length of the hypotenuse

Pythagoras's theorem states that: $hypotenuse=\sqrt{bas{e}^2+heigh{t}^2}$

Now, the hypotenuse will be,

$$\begin{gathered} hypotenuse=\sqrt{{\left(4\right)}^2+{\left(4\right)}^2} \\ \Rightarrow hypotenuse=\sqrt{16+16} \\ \Rightarrow hypotenuse=\sqrt{32}cm \end{gathered}$$

Hence, the correct option is (a) $\sqrt{32}cm$.