Question

find the missing side length in the triangle shown.
m = \sqrt{5}
m = 3\sqrt{5}
m = 5\sqrt{5}
m = 5\sqrt{3}

Explanation:

Step1: Apply Pythagorean theorem

Let the missing side be $m$. The theorem states $5^2 + m^2 = 10^2$.

Step2: Calculate squares

$25 + m^2 = 100$

Step3: Solve for $m^2$

$m^2 = 100 - 25 = 75$

Step4: Find $m$

$m = \sqrt{75} = 5\sqrt{3}$

Answer:

$m = 5\sqrt{3}$ (corresponding to the option with $m = 5\sqrt{3}$)