Chapter 11.8, Problem 15IP

a.

To determine

To find: Lengths of the segments $AC$ and $CB$

Answer to Problem 15IP

  $AC=6$

  $CB=8$

Explanation of Solution

From Given figure

We can say that

From $\Delta ABC$

  $AC=6$

  $CB=8$

b.

To determine

To find: Lengths of the segments $A\text{'}C\text{'}$ and $C\text{'}B\text{'}$

Answer to Problem 15IP

  $A\text{'}C\text{'}=3$

  $C\text{'}B\text{'}=4$

Explanation of Solution

From Given figure

We can say that

From $\Delta A\text{'}B\text{'}C\text{'}$

  $A\text{'}C\text{'}=3$

  $C\text{'}B\text{'}=4$

c.

To determine

To find: Values of $\frac{AC}{A\text{'}C\text{'}}$ , $\frac{CB}{C\text{'}B\text{'}}$ and $\frac{AB}{A\text{'}B\text{'}}$

Answer to Problem 15IP

  $\begin{array}{l}\frac{AB}{A\text{'}B\text{'}}=2\\ \frac{AC}{A\text{'}C\text{'}}=2\\ \frac{CB}{C\text{'}B\text{'}}=2\end{array}$

Explanation of Solution

From Given figure

We can say that

From $\Delta ABC$

  $AC=6$

  $CB=8$

  $AB=10$

From $\Delta A\text{'}B\text{'}C\text{'}$

  $A\text{'}C\text{'}=3$

  $C\text{'}B\text{'}=4$

  $A\text{'}B\text{'}=5$

Values of

  $\begin{array}{l}\frac{AB}{A\text{'}B\text{'}}=\frac{10}{5}\\ \Rightarrow \frac{AB}{A\text{'}B\text{'}}=2\end{array}$

  $\begin{array}{l}\frac{AC}{A\text{'}C\text{'}}=\frac{6}{3}\\ \Rightarrow \frac{AC}{A\text{'}C\text{'}}=2\end{array}$

  $\begin{array}{l}\frac{CB}{C\text{'}B\text{'}}=\frac{8}{4}\\ \Rightarrow \frac{CB}{C\text{'}B\text{'}}=2\end{array}$

Therefore,

We got

  $\begin{array}{l}\frac{AB}{A\text{'}B\text{'}}=2\\ \frac{AC}{A\text{'}C\text{'}}=2\\ \frac{CB}{C\text{'}B\text{'}}=2\end{array}$

d.

To determine

To find: What do you notice about the ratios.

Answer to Problem 15IP

On observing we can say that Value of all ratios are same that is $2$

  $\frac{AB}{A\text{'}B\text{'}}=\frac{AC}{A\text{'}C\text{'}}=\frac{CB}{C\text{'}B\text{'}}=2$

Explanation of Solution

From Given figure

We can say that

From $\Delta ABC$

  $AC=6$

  $CB=8$

  $AB=10$

From $\Delta A\text{'}B\text{'}C\text{'}$

  $A\text{'}C\text{'}=3$

  $C\text{'}B\text{'}=4$

  $A\text{'}B\text{'}=5$

Values of

  $\begin{array}{l}\frac{AB}{A\text{'}B\text{'}}=\frac{10}{5}\\ \Rightarrow \frac{AB}{A\text{'}B\text{'}}=2\end{array}$

  $\begin{array}{l}\frac{AC}{A\text{'}C\text{'}}=\frac{6}{3}\\ \Rightarrow \frac{AC}{A\text{'}C\text{'}}=2\end{array}$

  $\begin{array}{l}\frac{CB}{C\text{'}B\text{'}}=\frac{8}{4}\\ \Rightarrow \frac{CB}{C\text{'}B\text{'}}=2\end{array}$

On observing we can say that Value of all ratios are same that is $2$

  $\frac{AB}{A\text{'}B\text{'}}=\frac{AC}{A\text{'}C\text{'}}=\frac{CB}{C\text{'}B\text{'}}=2$