Question

Find the perimeter of the isosceles right angled triangle shown in the above figure if the length of its hypotenuse is given to be equal to $8\sqrt{2}$.

• A. 8
• B. $8+8\sqrt{2}$
• C. $8+16\sqrt{2}$
• D. 16
• E. $16+8\sqrt{2}$

Answer 1

The correct option is E $16+8\sqrt{2}$

In isosceles right angle triangle the length of the other sides $=$ $\frac{h}{\sqrt{2}}$

Let the sides is $x$, then

$\Rightarrow x=\frac{h}{\sqrt{2}}$

$\Rightarrow x=\frac{8\sqrt{2}}{\sqrt{2}}$

$\Rightarrow x=8$

Perimeter of isosceles right angled triangle $=$ $2x+h$

$\Rightarrow 2\times 8+8\sqrt{2}$

$\Rightarrow 16+8\sqrt{2}$