Question

find the length of the third side. if necessary, write in simplest radical form.

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle with legs $a$, $b$, hypotenuse $c$: $c^2=a^2+b^2$
Here $a=5$, $b=7$, so $c^2=5^2+7^2$

Step2: Calculate sum of squares

$5^2+7^2=25+49=74$

Step3: Solve for hypotenuse

$c=\sqrt{74}$

Answer:

$\sqrt{74}$