We are given a right triangle with one leg of length 5 and the hypotenuse of length $5\sqrt{5}$. We need to find the length of the other leg.

1. Problem Description

We are given a right triangle with one leg of length 5 and the hypotenuse of length $5\sqrt{5}$. We need to find the length of the other leg.

2. Solution Steps

Let the length of the unknown leg be $x$. We can use the Pythagorean theorem to solve for $x$. The Pythagorean theorem states that in a right triangle with legs $a$ and $b$ and hypotenuse $c$, we have $a^2 + b^2 = c^2$. In this case, $a = 5$, $b = x$, and $c = 5\sqrt{5}$. So we have:

$5^2 + x^2 = (5\sqrt{5})^2$

$25 + x^2 = 25 \cdot 5$

$25 + x^2 = 125$

$x^2 = 125 - 25$

$x^2 = 100$

$x = \sqrt{100}$

$x = 10$

3. Final Answer

10