Chapter 14.3, Problem 12PSB

To determine

To find the longer of the two medians.

Answer to Problem 12PSB

  $TN=18$

Explanation of Solution

Given:

The given figure of the triangle RST is-

  

  $\begin{array}{l}RP=2y-x,TP=2y\\ PM=y-2,PN=x+2\end{array}$

Calculation:

By using the theorem that the medians of a triangle that are concurrent at a point are two thirds of the way from any vertex of the triangle of the midpoint of the opposite side.

  $\begin{array}{l}RP=2PM\\ TP=2PN\\ \Rightarrow 2y-x=2(y-2)\\ 2y-x=2y-4\\ -x=-4\\ x=4\\ 2y=2(x+2)\\ y=x+2\\ y=4+2\\ y=6\\ \Rightarrow RM=RP+PM=2(6)-4+(6-2)=12\\ \Rightarrow TN=TP+PN=2(6)+(4+2)=18\end{array}$

The longer median is $TN=18$