Question

given trapezoid wxyz, what is xy? simplify your answer. (there is a diagram of trapezoid wxyz with segments labeled: wz is labeled \\(\frac{4}{3}xy\\), de is labeled 35 ft, and there are congruency marks on segments xd, d w, ye, and ez.)

Explanation:

Step1: Use the mid - segment theorem

In a trapezoid, the length of the mid - segment \(DE=\frac{1}{2}(WZ + XY)\). Let \(XY = x\). We know \(WZ=\frac{3}{4}x\) and \(DE = 35\).

Step2: Substitute into the formula

Substitute into \(DE=\frac{1}{2}(WZ + XY)\), we get \(35=\frac{1}{2}(\frac{3}{4}x+x)\).
First, simplify the right - hand side: \(\frac{1}{2}(\frac{3x + 4x}{4})=\frac{1}{2}\times\frac{7x}{4}=\frac{7x}{8}\).

Step3: Solve for \(x\)

Since \(\frac{7x}{8}=35\), then \(x = 35\times\frac{8}{7}\).
Calculate \(35\times\frac{8}{7}=\frac{35\times8}{7}=40\).

Answer:

\(40\)