Chapter 12, Problem 4CR

To determine

To Calculate:- Find PT and TR if PQ ¦ TR.

Answer to Problem 4CR

The length of the PT and TR would be $5\&\frac{32}{3}$ respectively.

Explanation of Solution

Given information : PQ ¦ TR.

Formula used : Use the property of Congruent Triangles.

Calculation: Triangles PQS and TRS are congruent.

From the figure

  $\begin{array}{l}\frac{PS}{QS}=\frac{TS}{RS}\hfill \\ \begin{array}{l}\frac{15}{18}=\frac{TS}{12}\\ TS=10\end{array}\hfill \\ \hfill \end{array}$

Now,

  $\begin{array}{l} PT=PS-TS\\ PT=15-10=5\end{array}$

Similarly,

  $\begin{array}{l}\frac{PQ}{QS}=\frac{TR}{RS}\\ \frac{16}{18}=\frac{TR}{12}\\ TR=\frac{32}{3}\end{array}$