Chapter 8, Problem 12RP

To determine

To calculate:The length of the ST, TV and PT segments.

Answer to Problem 12RP

The required lengths:

  $\begin{array}{l}ST=6.92\text{ units}\hfill \\ TV=3.08\text{ units}\hfill \\ PT=5.54\text{ units}\hfill \end{array}$

Explanation of Solution

Given information:

Two sides of triangles are parallel and lengths of sides

Formula used:

Compare the ratios of sides of triangles.

Calculation:

In triangles STP and SVW , we have

  $\begin{array}{l}\frac{ST}{SP}=\frac{SV}{SW}\\ \Rightarrow \frac{ST}{9}=\frac{10}{13}\\ \Rightarrow ST=9\times \frac{10}{13}\\ \Rightarrow ST=6.92\text{ units}\\ \therefore \\ TV=SV-ST\\ TV=10-6.92=3.08\end{array}$

Now again,

  $\begin{array}{l}\frac{\text{PT}}{\text{SP}}\text{=}\frac{\text{WV}}{\text{SW}}\\ \Rightarrow \frac{\text{PT}}{\text{9}}\text{=}\frac{\text{8}}{\text{13}}\\ \Rightarrow \text{PT=9}\times \frac{\text{8}}{\text{13}}=5,54\text{units}\end{array}$