Question

find the length of side x in simplest radical form with a rational denominator.

Explanation:

Step1: Identify the triangle type

This is a 45 - 45-90 right - triangle. In a 45 - 45-90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs are of equal length and the hypotenuse is $\sqrt{2}$ times the length of a leg. Let the length of each leg be $x$ and the hypotenuse be $h$. If one leg is $x$ and the other leg is $\sqrt{3}$, and since the legs of a 45 - 45-90 triangle are equal, we have $x = \sqrt{3}$.

Answer:

$\sqrt{3}$