Chapter 14.3, Problem 6PSA

a.

To determine

To find the length of AT.

Answer to Problem 6PSA

  $AT=6$

Explanation of Solution

Given:

The triangle is ABC as follows-

  

  $AM=9$

Calculation:

  $\begin{array}{l}\frac{AT}{TM}=\frac{AT}{9}=\frac{2}{3}\\ \Rightarrow AT=6\end{array}$

b.

To determine

To find the length of BN.

Answer to Problem 6PSA

  $BN=15$

Explanation of Solution

Given:

The triangle is ABC as follows-

  

  $TN=5$

Calculation:

  $\begin{array}{l}\frac{TN}{BN}=\frac{5}{BN}=\frac{1}{3}\\ \Rightarrow BN=15\end{array}$

c.

To determine

To find the length of AT.

Answer to Problem 6PSA

  $PT=4$

Explanation of Solution

Given:

The triangle is ABC as follows-

  

  $AM=9$

Calculation:

  $\begin{array}{l}\frac{TC}{PC}=\frac{8}{PC}=\frac{2}{3}\\ \Rightarrow PC=12\\ \frac{PT}{PC}=\frac{PT}{12}=\frac{1}{3}\\ 3PT=12\\ PT=4\end{array}$

d.

To determine

To find the length of TN.

Answer to Problem 6PSA

  $TN=\sqrt{2}$

Explanation of Solution

Given:

The triangle is ABC as follows-

  

  $BN=\sqrt{18}$

Calculation:

  $\begin{array}{l}\frac{TN}{BN}=\frac{TN}{\sqrt{18}}=\frac{1}{3}\\ \Rightarrow 3TN=\sqrt{18}\\ \Rightarrow TN=\frac{\sqrt{18}}{3}=\sqrt{2}\end{array}$