Question

given trapezoid wxyz, what is xy? xy = \boxed{\blacktriangle} (simplify your answer.)

Explanation:

Step1: Apply the mid - segment theorem of a trapezoid

The mid - segment (or midline) of a trapezoid is given by the formula \(DE=\frac{WZ + XY}{2}\), where \(DE\) is the mid - segment, \(WZ\) and \(XY\) are the bases of the trapezoid. We know that \(DE = 35\) and \(WZ=\frac{3}{4}XY\).
Substitute \(WZ=\frac{3}{4}XY\) into the formula: \(35=\frac{\frac{3}{4}XY+XY}{2}\).

Step2: Simplify the right - hand side of the equation

First, combine the terms in the numerator: \(\frac{3}{4}XY+XY=\frac{3}{4}XY+\frac{4}{4}XY=\frac{3 + 4}{4}XY=\frac{7}{4}XY\).
So the equation becomes \(35=\frac{\frac{7}{4}XY}{2}\).
Since \(\frac{\frac{7}{4}XY}{2}=\frac{7}{4}XY\times\frac{1}{2}=\frac{7}{8}XY\), we have the equation \(35=\frac{7}{8}XY\).

Step3: Solve for \(XY\)

Multiply both sides of the equation \(35=\frac{7}{8}XY\) by \(\frac{8}{7}\) to isolate \(XY\).
\(XY = 35\times\frac{8}{7}\).
We know that \(35\div7 = 5\), so \(35\times\frac{8}{7}=5\times8\).

Answer:

\(40\)