Chapter 8.5, Problem 22PSB

To determine

To find the length of a side.

Answer to Problem 22PSB

The length of XP is 6.66

Explanation of Solution

Given information:

  $\overrightarrow{VS}$ is parallel to $\overrightarrow{MR}$

  $\begin{array}{l}TV=12,VM=8,TS=15,\hfill \\ SR=TW=TX\hfill \end{array}$

Formula used:

The below property is used:

If a line is parallel to one side of triangle and intersects other sides, it divides sides proportionally.

Calculation:

  

It is given that,

  $\overrightarrow{VS}$ is parallel to $\overrightarrow{MR}$

  $\begin{array}{l}TV=12,VM=8,TS=15,\hfill \\ SR=TW=TX\hfill \end{array}$

If a line is parallel to one side of triangle and intersects other sides, it divides sides proportionally.

  $\begin{array}{l}\frac{TV}{TS}=\frac{VM}{SR}\\ \frac{12}{15}=\frac{8}{SR}\\ \therefore 12SR=120\\ \therefore SR=10\\ SinceSR=TX,TX=10\\ \frac{TX}{TS}=\frac{XP}{SR}\\ \frac{10}{15}=\frac{XP}{SR}\\ \therefore 15XP=100\\ \therefore XP=\frac{100}{15}=6.66\end{array}$