Question

find the length of side x in simplest radical form with a rational denominator. answer attempt 1 out of 2 x =

Explanation:

Step1: Identify the triangle type

This is a right - isosceles triangle. In a right - isosceles triangle, the two legs are of equal length. Let the length of each leg be $a$. Using the Pythagorean theorem $a^{2}+a^{2}=x^{2}$, where one leg $a = \sqrt{12}$.

Step2: Apply the Pythagorean theorem

If $a=\sqrt{12}$, then $(\sqrt{12})^{2}+(\sqrt{12})^{2}=x^{2}$. Since $(\sqrt{12})^{2}=12$, we have $12 + 12=x^{2}$, so $x^{2}=24$.

Step3: Solve for $x$

Taking the square root of both sides, $x=\sqrt{24}$. Simplify $\sqrt{24}=\sqrt{4\times6}=2\sqrt{6}$.

Answer:

$2\sqrt{6}$