Chapter 6.4, Problem 4E

To determine

To find: ratio of the lengths of corresponding sides.

Answer to Problem 4E

Theratio of the lengths is $\frac{1}{1.5}$ .

Explanation of Solution

Given information: From the diagram provided in the question, $\Delta ABC\sim \Delta DEF$

  $\begin{array}{l}AB=4\text{ cm}\\ BC=3\text{ cm}\\ AC=5\text{ cm}\\ DF=7.5\text{ cm}\\ DE=6\text{ cm}\\ EF=4.5\text{ cm}\end{array}$

Calculation:

The corresponding sides of the similar triangles are:

  $\text{AB and DE, BC and EF},\text{AC and DF}$

  $\text{So, Ratio of AB and DE}$

  $\frac{AB}{DE}=\frac{4}{6}$

Ratio of BC and EF

  $\frac{BC}{EF}=\frac{3}{4.5}$

Ratio of AC and DF

  $\frac{AC}{DF}=\frac{5}{7.5}$

Therefore, the ratios of corresponding sides of similar triangles is equal

  $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{1}{1.5}$

Hence , the answer is $\frac{1}{1.5}$