Chapter 7.3, Problem 24WE

To determine

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

Answer to Problem 24WE

Thevalues of $x,y\text{and}z$ are $28,24\text{and}36$ 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, $\frac{20}{15}=\frac{x}{21}=\frac{y}{18}=\frac{z}{27}$

  $\begin{array}{l}\Rightarrow \frac{4}{3}=\frac{x}{21}=\frac{y}{18}=\frac{z}{27}\\ \Rightarrow \frac{4}{3}=\frac{x}{21},\frac{4}{3}=\frac{y}{18},\frac{4}{3}=\frac{z}{27}\\ \Rightarrow x=\frac{4}{3}\times 21,y=\frac{4}{3}\times 18,z=\frac{4}{3}\times 27\\ \therefore x=28,y=24,z=36.\end{array}$

Hence, thevalues of $x,y\text{and}z$ are $28,24\text{and}36$ respectively.