Question

this is a 45 - 45 - 90 triangle. what is the measure of x? √13 x x = √?

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

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 $x$. Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, with $a = x$, $b = x$ and $c=\sqrt{13}$.

Step2: Apply Pythagorean theorem

We have $x^{2}+x^{2}=(\sqrt{13})^{2}$. Combining like - terms, $2x^{2}=13$. Then $x^{2}=\frac{13}{2}$.

Answer:

$x = \sqrt{\frac{13}{2}}$