Chapter 9, Problem 24RP

a.

To determine

Tocalculate:The value of x .

Answer to Problem 24RP

The value of x is 4.5.

Explanation of Solution

Given information:

Side $AC=10,$

Side $DC=8.$

  $\overline{AD}\perp \overline{BC}$

Formula used:

The below property is used:

Corresponding sides of similar triangles are congruent.

Calculation:

  

  $\Delta ADE\sim \Delta BAC$

Corresponding sides of similar triangles are congruent.

  $\begin{array}{l}\frac{DC}{AC}=\frac{AC}{8+x}\\ \frac{8}{10}=\frac{10}{8+x}\\ 100=64+8x\\ 36=8x\\ \therefore x=\frac{36}{8}=4.5\end{array}$

b.

To determine

To find: The value of y .

Answer to Problem 24RP

The value of yis 3.

Explanation of Solution

Given information:

Side $AC=10,$

Side $DC=8.$

  $\overline{AD}\perp \overline{BC}$

Formula used:

The below property is used:

Corresponding sides of similar triangles are congruent.

Calculation:

  

  $\Delta ADC\sim \Delta BAC$

Corresponding sides of similar triangles are congruent.

  $\begin{array}{l}\frac{BD}{AB}=\frac{AB}{BC}\\ \frac{y}{6}=\frac{6}{y+9}\\ 36=y^2+9y\\ y^2+9y-36=0\\ (y+12)(y-3)=0\\ y=-12ory=3\end{array}$

Length cannot be negative.

  $\therefore y=3$