Question

In the diagram below of triangle MNP, Q is a midpoint of M N and R is a midpoint of NP. If QR = 76 - 8x, and MP = 89 - 9x, what is the measure of MP? N R M Р

Answer 1

Given that Q and R are midpoints, then segment QR is half of segment MP.

$QR=\frac{1}{2}MP$

Substituting with data,

$\begin{gathered} 76-8x=\frac{1}{2}(89-9x) \\ 76-8x=\frac{1}{2}\cdot89-\frac{1}{2}9x \\ 76-8x=\frac{89}{2}-\frac{9}{2}x \\ 76-\frac{89}{2}=-\frac{9}{2}x+8x \\ \frac{76\cdot2-89}{2}=\frac{-9+8\cdot2}{2}x \\ \frac{63}{2}=\frac{7}{2}x \\ \frac{63}{2}\cdot\frac{2}{7}=x \\ 9=x \end{gathered}$

Therefore, the measure of MP is:

MP = 89 - 9x

MP = 89 - 9*9

MP = 89 - 81

MP = 8