Chapter 12.4, Problem 3MRE

To determine

To find : The value of x, y, z.

Answer to Problem 3MRE

The value of x , y, and z are 15, 6 and 9 respectively.

Explanation of Solution

Given information :

The given diagram is

Calculation :

The scale factor of the trapezoid is given by the ratio of their corresponding sides.

Here, AD and PS are corresponding sides and $PS=18$ and $AD=12$ .

Therefore, scale factor is

  $\begin{array}{l}\text{Scale factor}=\frac{PS}{AD}\\ \text{Scale factor}=\frac{18}{12}\\ \text{Scale factor}=1.5\end{array}$

Now, multiply the scale factor with each of the corresponding sides of x , y and z.

Therefore,

  $\begin{array}{l}x=10\cdot 1.5\\ x=15\end{array}$

  $\begin{array}{l}y=4\cdot 1.5\\ y=6\end{array}$ and

  $\begin{array}{l}z=6\cdot 1.5\\ y=9\end{array}$

Hence,

The value of x , y, and z are 15, 6 and 9 respectively.