Question

find k.

write your answer in simplest radical form.

yards

Explanation:

Step1: Identify triangle type

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

Step2: Relate given side to $k$

The given side $2\sqrt{2}$ is the hypotenuse, so set up the equation:
$k\sqrt{2} = 2\sqrt{2}$

Step3: Solve for $k$

Divide both sides by $\sqrt{2}$:
$k = \frac{2\sqrt{2}}{\sqrt{2}} = 2$

Answer:

2 yards