Chapter 5.5, Problem 30WE

To determine

ToFind: that $ME,FN\text{ and }EF$ shown in figure such that ABCD is trapezoid with median MN, $DC=6\text{ and }AB=16$ .

Answer to Problem 30WE

  $ME=3$ , $FN=3$ and $EF=5$ .

Explanation of Solution

Given

Figure is shown as.

  

ABCD is trapezoid with median MN, $DC=6\text{ and }AB=16$ .

Calculation:

Since, MN is a median therefore.

  $\begin{array}{l}ME=\frac{1}{2}DC\\ ME=\frac{1}{2}\times 6\\ ME=3\end{array}$

  $\begin{array}{l}FN=\frac{1}{2}DC\\ FN=\frac{1}{2}\times 6\\ FN=3\end{array}$

Now,

  $\begin{array}{l}EF=\frac{1}{2}\left(AB-DC\right)\\ EF=\frac{1}{2}\left(16-6\right)\\ EF=5\end{array}$

Therefore, the answer is $ME=3$ , $FN=3$ and $EF=5$ .