Question

the hypotenuse of an isosceles triangles 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 $x$. In an isosceles right - triangle, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, and since $a = b=x$ and $c$ is the hypotenuse, we have $x^{2}+x^{2}=c^{2}$, which simplifies to $2x^{2}=c^{2}$.

Step2: Substitute the value of the hypotenuse

Given $c = 10$. So, $2x^{2}=10^{2}=100$.

Step3: Solve for $x$

First, divide both sides of the equation $2x^{2}=100$ by 2: $x^{2}=50$. Then, take the square root of both sides: $x=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}=\frac{10}{\sqrt{2}}$.

Answer:

$\frac{10}{\sqrt{2}}$