Chapter 1.2, Problem 24PPS

To determine

To find: The value of the variable and $YZ$ .

Answer to Problem 24PPS

The segment $YZ$ is $16$ , and the variable $d$ is $2$ .

Explanation of Solution

Given information:

The given segments are $XY=11d$ , $YZ=9d-2$ , and $XZ=5d+28$ .

  

Calculation:

Calculate the value of the segment and the variable.

  $\begin{array}{c}XZ=XY+YZ\\ 5d+28=11d+9d-2\\ 20d-5d=28+2\\ 15d=30\\ d=2\end{array}$

Thus,

  $\begin{array}{c}YZ=9d-2\\ =9\left(2\right)-2\\ =16\end{array}$

Therefore, the segment $YZ$ is $16$ , and the variable $d$ is $2$ .