Chapter 7.3, Problem 25WE

To determine

To find the values of $x,y,z$ .

Answer to Problem 25WE

Thevalues of $x,y\text{and}z$ are $8,18\text{and}12$ respectively.

Explanation of Solution

Given information:

The following two similar polygons are provided

  

Since given two polygons are similar, so their corresponding sides are in equal proportions.

Thus, $\frac{10}{15}=\frac{x}{12}=\frac{12}{y}=\frac{z}{18}$

  $\begin{array}{l}\Rightarrow \frac{2}{3}=\frac{x}{12}=\frac{12}{y}=\frac{z}{18}\\ \Rightarrow \frac{2}{3}=\frac{x}{12},\frac{2}{3}=\frac{12}{y},\frac{2}{3}=\frac{z}{18}\\ \Rightarrow x=\frac{2}{3}\times 12,y=\frac{3}{2}\times 12,z=\frac{2}{3}\times 18\\ \therefore x=8,y=18,z=12.\end{array}$

Hence, thevalues of $x,y\text{and}z$ are $8,18\text{and}12$ respectively.