find g. write your answer in simplest radical form. yards

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the hypotenuse $c$ is related to the legs $a$ and $b$ (which are equal) by $c = a\sqrt{2}$ or $c = b\sqrt{2}$.

Step2: Set up the equation

Let the length of each leg be $g$. The hypotenuse $c = 2\sqrt{2}$. Using the 45 - 45 - 90 triangle ratio $c = g\sqrt{2}$. Substitute $c = 2\sqrt{2}$ into the equation: $2\sqrt{2}=g\sqrt{2}$.

Step3: Solve for $g$

Divide both sides of the equation $2\sqrt{2}=g\sqrt{2}$ by $\sqrt{2}$. We get $g=\frac{2\sqrt{2}}{\sqrt{2}} = 2$.

Answer:

$2$