Question

1. solve for the missing side. do the side lengths form a pythagorean triple?

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, if the hypotenuse is 13 mi and one leg is 5 mi, then $x=\sqrt{13^{2}-5^{2}}$.

Step2: Calculate the value of $x$

$x=\sqrt{169 - 25}=\sqrt{144}=12$ mi.

Step3: Check Pythagorean triple

A Pythagorean triple is a set of three positive integers $a$, $b$, $c$ such that $a^{2}+b^{2}=c^{2}$. Here, $5^{2}+12^{2}=25 + 144=169=13^{2}$, so the side - lengths form a Pythagorean triple.

Answer:

$x = 12$ mi
Yes