Chapter 9.3, Problem 17PSB

(a)

To determine

To find: The length of a line segment $CD$ .

Answer to Problem 17PSB

The length of line segment $CD= 2\sqrt{7}\text{ units}$

Explanation of Solution

Given information :

  $AD=7\text{ units and }AB=11\text{ units}$

Formula used :

  ${\left(CD\right)}^2=AD\times DB$

Calculation :

  $\begin{array}{l}{\left(CD\right)}^2=AD\times DB\\ =7\times (AB-AD)\\ =7\times \left(11-7\right)\\ =28\\ \Rightarrow CD=2\sqrt{7}\text{ units}\end{array}$

(b)

To determine

To find: The length of a line segment $AB$ .

Answer to Problem 17PSB

The length of the line segment $AB= 14\text{ units}$

Explanation of Solution

Given information :

  $CD=8\text{ units and }AD=6\text{ units}$

Formula used :

  ${\left(CD\right)}^2=AD\times DB$

Calculation :

  $\begin{array}{l}{\left(CD\right)}^2=AD\times DB\\ $ \Rightarrow {(8)}^2=6\times DB$\Rightarrow DB=\frac{48}{6}=8\\ AB=AD+BD=6+8=14\text{ units}\end{array}$

(c)

To determine

To find: The length of a line segment $BC$ .

Answer to Problem 17PSB

The length of the line segment $BC\text{ is }4\sqrt{3}\text{ units}$

Explanation of Solution

Given information :

  $AB=12\text{units},AD=4\text{units}$

Formula used :

  ${\left(BC\right)}^2=AB\times DB$

Calculation :

  $\begin{array}{l}{\left(BC\right)}^2=AB\times DB\\ {\left(BC\right)}^2=12\times 4=48\\ \Rightarrow BC=4\sqrt{3}\text{ units}\end{array}$

(d)

To determine

To find: The length of a line segment $BD$

Answer to Problem 17PSB

The length of the line segment $BD= 7\frac{11}{12}\text{ units}$

Explanation of Solution

Given information :

  $AC=7\text{ units and }AB=12\text{ units}$

Formula used :

  ${\left(AC\right)}^2=AB\times AD$

Calculation :

  $\begin{array}{l}{\left(AC\right)}^2=AB\times AD\\ 7^2=12(AB-BD)\\ 49=12(12-BD)\\ \Rightarrow BD=\frac{144-49}{12}=\frac{95}{12}=7\frac{11}{12}\text{ units}\end{array}$