Chapter 8.5, Problem 29PSC

To determine

To show that the given information is impossible.

Answer to Problem 29PSC

The given information is not correct.

Explanation of Solution

Given information:

  $\overleftrightarrow{RW}$ bisects $\angle SRT$ .

  $\overleftrightarrow{TV}$ bisects $\angle RTS$ .

  $\begin{array}{l}RV=4,\\ SV=5,\\ SW=6,\\ WT=7\end{array}$

Formula used:

The below theorem is used:

Angle bisector theorem states that an angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

Calculation:

  

Using Angle Bisector Theorem, for $\angle R$ we get

  $\begin{array}{l}\frac{SW}{WT}=\frac{RS}{RT}\\ \\ \frac{6}{7}=\frac{9}{RT}\\ \\ 6RT=63\\ \\ RT=10.5\end{array}$

Now, for the $\angle T$

  $\begin{array}{l}\frac{RV}{VS}=\frac{RT}{TS}\\ \\ \frac{4}{5}=\frac{RT}{13}\\ \\ 5RT=52\\ \\ RT=10.4\end{array}$

But RT cannot have two different lengths, therefore the given information is not correct.