question\nfind the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the hypotenuse

The hypotenuse is the longest side of a right - triangle. Here, the hypotenuse $c = 13$ and one side $a = 12$.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a,b$ are the other two sides. We want to find $b$, so $b=\sqrt{c^{2}-a^{2}}$. Substitute $c = 13$ and $a = 12$ into the formula: $b=\sqrt{13^{2}-12^{2}}=\sqrt{(13 + 12)(13 - 12)}=\sqrt{25\times1}=\sqrt{25}=5$.

Answer:

5