Chapter 8.2, Problem 9PSB

To determine

To calculate:The sides of given similar triangles.

Answer to Problem 9PSB

The required sides of given similar triangles are

5.6 units and 7.5 units

Explanation of Solution

Given information

  $\Delta \text{SVT}\sim \Delta \text{WYX}$

Measures of sides of triangle

SV = 7 units, ST = 10 units, YX = 6 units and WX = 8 units

Formula used In similar triangles, ratios of corresponding sides are equivalent

Calculation In similar triangles, $\Delta \text{SVT}\sim \Delta \text{WYX}$ , we have

  $\begin{array}{l}\frac{\text{WY}}{\text{WX}}=\frac{\text{SV}}{\text{ST}}\\ \Rightarrow \text{WY=WX}\times \frac{\text{SV}}{\text{ST}}=8\times \frac{7}{10}=5.6\text{ units}\end{array}$

And further we have,

  $\begin{array}{l}\frac{\text{VT}}{\text{ST}}=\frac{\text{YX}}{\text{WX}}\\ \Rightarrow \text{VT=ST}\times \frac{\text{YX}}{\text{WX}}=10\times \frac{6}{8}=7.5\text{ units}\end{array}$