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 ratio for 45 - 45 - 90 triangle

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

Step2: Solve for the leg length

We know $c = 128$ cm. Rearranging the formula $c = a\sqrt{2}$ to solve for $a$, we get $a=\frac{c}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{128}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{128\sqrt{2}}{2}=64\sqrt{2}$ cm.

Answer:

B. $64\sqrt{2}$ cm