Question

What is the perimeter, in inches, of the isosceles right triangle shown below, whose hypotenuse is $8\sqrt{2}$ inches long?

• 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 $16+8\sqrt{2}$

Isosceles triangle is when two sides are equal.

Let the two sides are of equal length be $a$.

In a right angled isosceles triangle,

$a^2{+}^2=h^2$ Where $h$ is hypotenuse of triangle.

$\Rightarrow 2a^2=h^2$

Given that $h=8\sqrt{2}$

$\Rightarrow 2a^2={\left(8\sqrt{2}\right)}^2$

$\Rightarrow a=\sqrt{\frac{128}{2}}=8$

Side of traingle is $a=8$

Perimeter of triangle $a+a+h$

$\Rightarrow 2a+h$

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

Perimeter $=16+8\sqrt{2}$