Question

find s.
$2\sqrt{6}$ km
write your answer in simplest radical form.
kilometers

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so the two legs are equal, and hypotenuse = $s\sqrt{2}$, where $s$ is a leg length.

Step2: Set up hypotenuse equation

Given hypotenuse = $2\sqrt{6}$, so:
$$2\sqrt{6} = s\sqrt{2}$$

Step3: Solve for $s$

Isolate $s$ by dividing both sides by $\sqrt{2}$, then rationalize:
$$s = \frac{2\sqrt{6}}{\sqrt{2}} = 2\sqrt{\frac{6}{2}} = 2\sqrt{3}$$

Answer:

$2\sqrt{3}$ kilometers