Question

In the following figure, a trapezoid$ABCD$has a median$\overline{MN}$ . If $DC=42,MN=35$ then find $AB$.

Short answer

The measure of$AB=28$units.

Step-by-step solution

Step 1- Apply the concept of midsegment theorem.

The trapezoid midsegment theorem states that the length of the midsegment is equal to the sum of the base lengths divided by 2.

Step 2- Check the figure.

Consider the figure.

Step 3- Step description.

Here$MN$ is the median and $DC=42,MN=35$.

Use the mid-segment theorem and find the value of $AB$ as follows:

$\begin{array}{c}MN=\frac{AB+DC}{2}\\ 35=\frac{AB+42}{2}\\ AB+42=70\\ AB=28\end{array}$

Therefore, the measure of $AB=28$units.