Question

find the length of the third side. if necessary, write in simplest radical form.
10
$10\sqrt{2}$

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ is hypotenuse, $a,b$ are legs. Let unknown side be $x$.

Step2: Substitute known values

$10^2 + x^2 = (10\sqrt{2})^2$

Step3: Calculate squared terms

$100 + x^2 = 100 \times 2 = 200$

Step4: Solve for $x^2$

$x^2 = 200 - 100 = 100$

Step5: Find square root of $x^2$

$x = \sqrt{100} = 10$

Answer:

10