Chapter 8.5, Problem 10PSA

To determine

To find the value of two sides.

Answer to Problem 10PSA

The value of SV is 3.46 and VT is 2.4

Explanation of Solution

Given information:

  $\overleftrightarrow{SV}$ is parallel to $\overleftrightarrow{RW}$

  $\begin{array}{l}RW=15,\\ RS=10,\\ ST=3,\\ WV=8\end{array}$

Formula used:

The below properties are used:

If the lines are parallel then their corresponding angles are congruent.

Corresponding sides of similar triangles are proportional.

Calculation:

  

It is given that,

  $\overleftrightarrow{SV}$ is parallel to $\overleftrightarrow{RW}$

  $\begin{array}{l}RW=15,\\ RS=10,\\ ST=3,\\ WV=8\end{array}$

If the lines are parallel then their corresponding angles are congruent.

  $\begin{array}{l}\angle TSV\cong \angle TRW\\ \angle TVS\cong \angle TWR\end{array}$

By AA similarity rule, we get

  $\Delta TVS~\Delta TWR$

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}\frac{TS}{SV}=\frac{TR}{RW}\\ \frac{3}{SV}=\frac{13}{15}\\ 13(SV)=45\\ \therefore SV=3.46\end{array}$

  $\begin{array}{l}\frac{RS}{ST}=\frac{WV}{VT}\\ \frac{10}{3}=\frac{8}{VT}\\ 10(VT)=24\\ \therefore VT=2.4\end{array}$