Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be $c$, the two legs are $a=7$ and $b=\sqrt{51}$. The Pythagorean theorem is $c^2 = a^2 + b^2$.

Step2: Calculate squares of known sides

$a^2 = 7^2 = 49$, $b^2 = (\sqrt{51})^2 = 51$

Step3: Sum the squared values

$c^2 = 49 + 51 = 100$

Step4: Solve for $c$

$c = \sqrt{100} = 10$

Answer:

10