the hypotenuse of a 45° - 45° - 90° triangle measures 128 cm. what is the length of one leg of the triangle…
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
Answer
Answer:
B. $64\sqrt{2}\text{ cm}$
Explanation:
Step1: Recall ratio for 45 - 45 - 90 triangle
In a 45 - 45 - 90 triangle, if leg length is $a$, hypotenuse $c = a\sqrt{2}$.
Step2: Solve for leg length
Given $c = 128$, then $a=\frac{c}{\sqrt{2}}$. Rationalize denominator: $a=\frac{128}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{128\sqrt{2}}{2}=64\sqrt{2}$.