Question

solve for n and m
answer attempt 1 out of 3
n =
m =

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $a:a:a\sqrt{2}$, where the legs are of length $a$ and the hypotenuse is of length $a\sqrt{2}$.

Step2: Find the length of the leg $n$

Given one leg is $2\sqrt{2}$. Since the two legs of a 45 - 45 - 90 triangle are equal, $n = 2\sqrt{2}$.

Step3: Find the length of the hypotenuse $m$

Using the ratio, if the leg length $a = 2\sqrt{2}$, then the hypotenuse $m=a\sqrt{2}=(2\sqrt{2})\times\sqrt{2}=4$.

Answer:

$n = 2\sqrt{2}$
$m = 4$