Chapter 9, Problem 16RP

a.

To determine

To find: Thelength of sideCB .

Answer to Problem 16RP

The length of sideCB is 8.

Explanation of Solution

Given information:

  $\begin{array}{l}AC\perp CB.\\ DE\parallel CB.\end{array}$

Side $AC=15,$

Side $AB=17,$

Side $DE=4.$

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

Side CB can be calculated by applying Pythagoras Theorem.

In right angled $\Delta ABC$ , we get

  $\begin{array}{l}{\left(AB\right)}^2={\left(AC\right)}^2+{\left(CB\right)}^2\\ {\left(17\right)}^2={\left(15\right)}^2+{\left(CB\right)}^2\\ {\left(CB\right)}^2=289-225\\ {\left(CB\right)}^2=64\\ \therefore CB=8\end{array}$

b.

To determine

Tocalculate: The length of sideAD .

Answer to Problem 16RP

The length of sideAD is 7.5.

Explanation of Solution

Given information:

  $\begin{array}{l}AC\perp CB.\\ DE\parallel CB.\end{array}$

Side $AC=15,$

Side $AB=17,$

Side $DE=4.$

Formula used:

The below property is used:

Corresponding sides of similar triangles are congruent.

Calculation:

  

  $\Delta ADE\sim \Delta ADE$

Corresponding sides of similar triangles are congruent.

  $\begin{array}{l}\frac{AD}{DE}=\frac{AC}{CB}\\ \frac{AD}{4}=\frac{15}{8}\\ 8(AD)=60\\ AD=\frac{60}{8}=7.5\end{array}$

c.

To determine

Tocalculate: The length of sideAE .

Answer to Problem 16RP

The length of side AE is 8.5.

Explanation of Solution

Given information:

  $\begin{array}{l}AC\perp CB.\\ DE\parallel CB.\end{array}$

Side $AC=15,$

Side $AB=17,$

Side $DE=4.$

Formula used:

The below property is used:

Corresponding sides of similar triangles are congruent.

Calculation:

  

  $\Delta AED\sim \Delta ABE$

Corresponding sides of similar triangles are congruent.

  $\begin{array}{l}\frac{AE}{DE}=\frac{AB}{CB}\\ \frac{AE}{4}=\frac{17}{8}\\ 8(AE)=68\\ AD=\frac{68}{8}=8.5\end{array}$

d.

To determine

To find:The length of sideEB .

Answer to Problem 16RP

The length of side EB is 8.5.

Explanation of Solution

Given information:

  $\begin{array}{l}AC\perp CB.\\ DE\parallel CB.\end{array}$

Side $AC=15,$

Side $AB=17,$

Side $DE=4.$

Formula used:

The below property is used:

A length of a line can be calculated by knowing the length difference of other two lines.

Calculation:

  

  $\begin{array}{l}EB=AB-AE\\ EB=17-8.5\\ EB=8.5\end{array}$

e.

To determine

Tocalculate: The length of sideDC .

Answer to Problem 16RP

The length of side DC is 7.5

Explanation of Solution

Given information:

  $\begin{array}{l}AC\perp CB.\\ DE\parallel CB.\end{array}$

Side $AC=15,$

Side $AB=17,$

Side $DE=4.$

Formula used:

The below property is used:

A length of a line can be calculated by knowing the difference of other two lines.

Calculation:

  

  $\begin{array}{l}DC=AC-AD\\ DC=15-7.5\\ DC=7.5\end{array}$