Question

the hypotenuse of an isosceles triangle measures 10 inches long. what is the length of one leg of the triangle?
10\sqrt{2}
10\sqrt{3}
\frac{10}{\sqrt{2}}
\frac{10}{\sqrt{3}}

Explanation:

Step1: Recall Pythagorean theorem for isosceles right - triangle

Let the length of each leg be $a$. In an isosceles right - triangle, by the Pythagorean theorem $c^{2}=a^{2}+a^{2}$, where $c$ is the hypotenuse. Since $c = 10$ and $c^{2}=2a^{2}$, we have $10^{2}=2a^{2}$.

Step2: Solve for $a$

$100 = 2a^{2}$, then $a^{2}=50$. Taking the square - root of both sides, $a=\sqrt{50}=\frac{10}{\sqrt{2}}$. Rationalizing the denominator, $a = 5\sqrt{2}=\frac{10}{\sqrt{2}}$.

Answer:

None of the given options are correct. The length of one leg is $5\sqrt{2}$ or $\frac{10}{\sqrt{2}}$.