Question

For trapezoid WXYZ shown below, points U and V are the midpoints of the legs. Use this information to find UV, the length of the mid segment.

Answer 1

Given:

$\begin{gathered} WX=x+7 \\ ZY=6x+5 \\ UV=8x-3 \end{gathered}$$\begin{gathered} UV=\frac{1}{2}(WX+ZY) \\ 8x-3=\frac{1}{2}(x+7+6x+5) \\ 2(8x-3)=(7x+12) \\ 16x-6=7x+12 \\ 16x-7x=12+6 \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}$$\begin{gathered} \text{Length of the midsegment=8x-3} \\ =8(2)-3 \\ =16-3 \\ =13 \end{gathered}$

13 is the final answer.