Question

Each diagram shows a trapezoid and its median. Find the value of x.

Short answer

The value of x is 5.

Step-by-step solution

Step 1. Label the diagram.

Step 2. Apply the property of trapezoid.

The length of the median of the trapezoid is equal to the average length of the two bases.

From the given figure it can be observed that XY is the median and $\text{ABandCD}$are the two bases of the trapezoid. Therefore, the length of the median is given by

$XY=\frac{1}{2}\left(AB+CD\right)$

Step 3. Description of step.

Substitute $3x+2$ for AB, $2x+1$for CD and $2x+4$for XY into equation obtained in step 2 to find the value of x.

$\begin{array}{c}2x+4=\frac{1}{2}\left(3x+2+2x+1\right)\\ 2x+4=\frac{1}{2}\left(5x+3\right)\\ 4x+8=5x+3\\ x=5\end{array}$

Therefore, the value of x is 5.