Question

find m.
3√6 m
45°
45°
m
write your answer in simplest radical form.
meters

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so the two legs are equal, and the hypotenuse is leg $\times \sqrt{2}$. The given side $3\sqrt{6}$ is the hypotenuse, and $m$ is a leg.

Step2: Set up equation

Let the leg length be $m$. The hypotenuse formula gives:
$$3\sqrt{6} = m\sqrt{2}$$

Step3: Solve for $m$

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

Answer:

$3\sqrt{3}$ meters