Question

the hypotenuse of a 45 - 45 - 90 triangle measures 128 cm. what is the length of one leg of the triangle? 64 cm 64√2 cm 128 cm 128√2 cm

Explanation:

Step1: Recall 45 - 45 - 90 ratio

In a 45 - 45 - 90 triangle, if the hypotenuse is $c$ and the leg is $a$, $c = a\sqrt{2}$.

Step2: Solve for leg length

Given $c = 128$, then $a=\frac{c}{\sqrt{2}}=\frac{128}{\sqrt{2}} = 64\sqrt{2}$.

Answer:

$64\sqrt{2}\text{ cm}$