Question

what is the length of each leg of the triangle below? a. $sqrt{32}$ b. 1 c. $16sqrt{2}$ d. 16 e. $4sqrt{2}$ f. 5.6

Explanation:

Step1: Identify triangle type

It's a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, if the hypotenuse is $c$ and the legs are $a$ and $b$ (and $a = b$), the ratio is $a:b:c=1:1:\sqrt{2}$.

Step2: Set up equation

Let the length of each leg be $x$. Given $c = 32$, and $c=\sqrt{2}x$. So, $32=\sqrt{2}x$.

Step3: Solve for $x$

$x=\frac{32}{\sqrt{2}}=\frac{32\sqrt{2}}{2}=16\sqrt{2}$.

Answer:

C. $16\sqrt{2}$