Question

the hypotenuse of a 45° - 45° - 90° triangle measures 10√5 in. what is the length of one leg of the triangle? 5√5 5√10 10√5 10√10

Explanation:

Step1: Recall the ratio of sides in 45 - 45 - 90 triangle

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

Step2: Solve for the leg length $a$

Given $c = 10\sqrt{5}$, and $c=a\sqrt{2}$. So, $a=\frac{c}{\sqrt{2}}$. Substitute $c = 10\sqrt{5}$ into the formula: $a=\frac{10\sqrt{5}}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{10\sqrt{5}\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{10\sqrt{10}}{2}=5\sqrt{10}$.

Answer:

B. $5\sqrt{10}$