Chapter 6, Problem 4E

To determine

To calculate:The length of segment DE in a $\Delta DEF$ , where $DF=7.5cm$ . Also, $\Delta DEF$ is similar to $\Delta ABC$ . In $\Delta ABC$ , $AB=5cm$ , $BC=3cm$ and $AC=6cm$ .

Answer to Problem 4E

The length of segment DE in $\Delta DEF$ is $6.25cm$

Explanation of Solution

Given information:

In $\Delta ABC$ , $AB=5cm$ , $BC=3cm$ and $AC=6cm$ .

  $\Delta ABC\sim \Delta DEF$

  $DF=7.5cm$

Formula Used:

If, $\Delta ABC\sim \Delta DEF$ , then $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Calculation:

It is given that

In $\Delta ABC$ , $AB=5cm$ , $BC=3cm$ and $AC=6cm$

  $\Delta ABC\sim \Delta DEF$ ,

And $DF=7.5cm$

As per the formula, if $\Delta ABC\sim \Delta DEF$ , then $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Using $\frac{AB}{DE}=\frac{AC}{DF}$

  $\frac{5}{DE}=\frac{6}{7.5}$

Simplifying further,

  $DE=6.25$

Hence, the length of segment DE in $\Delta DEF$ is $6.25cm$