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=(1)/(2)MP`

Substituting with data,

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