Question

given trapezoid wxyz, what is xy? xy = (simplify your answer.)

Explanation:

Step1: Set up equation

Let $XY = x$. We know that $WZ=\frac{4}{3}x$ and by the mid - segment formula for a trapezoid, the length of the mid - segment $DE=\frac{XY + WZ}{2}$. Given $DE = 28$ ft. So, $28=\frac{x+\frac{4}{3}x}{2}$.

Step2: Simplify the right - hand side

First, combine like terms in the numerator: $x+\frac{4}{3}x=\frac{3x + 4x}{3}=\frac{7x}{3}$. Then the equation becomes $28=\frac{\frac{7x}{3}}{2}=\frac{7x}{6}$.

Step3: Solve for x

Cross - multiply: $7x=28\times6$. So, $7x = 168$. Divide both sides by 7: $x=\frac{168}{7}=24$.

Answer:

24