Chapter 8.2, Problem 4PSA

To determine

To calculate: The length of unknown side of the given triangle

Answer to Problem 4PSA

The length of unknown side of the given triangle is 5 units

Explanation of Solution

Given information

Triangles are similar and measurements of known sides are given

Formula used

Ratios of corresponding sides are equal in similar triangles

Calculation

Given,

  $\Delta \text{ABC }\sim \Delta \text{DEF}$

  $\begin{array}{l}\therefore \frac{\text{EF}}{\text{BC}}=\frac{\text{DE}}{\text{AB}}\\ \Rightarrow \frac{\text{EF}}{\text{4}}=\frac{\text{10}}{\text{8}}\\ \Rightarrow \text{EF=4}\times \frac{10}{8}=5\text{ units}\end{array}$