Chapter 8.4, Problem 8PSA

To determine

To find the value of three sides.

Answer to Problem 8PSA

The value of OP is 8, PR = 4 and MR is 5.33

Explanation of Solution

Given information:

  $GJKL~MOPR$

Formula used:

The below properties are used:

Corresponding sides of similar triangles are proportional.

Means extremes product theorem:

If a product of a pair of not zero numbers is equal to the product of another pair of not zero numbers, then either pair of numbers be made the extremes, and the other pair the means, of proportion.

Calculation:

It is given that,

  $GJKL~MOPR$

  

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}GJ/MO=JK/OP\\ 9/6=12/OP\end{array}$

Applying means extremes product theorem, we get

  $\begin{array}{l}9*OP=72\\ \therefore OP=18\end{array}$

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}GJ/MO=LK/PR\\ 9/6=6/PR\end{array}$

Applying means extremes product theorem, we get

  $\begin{array}{l}9*PR=36\\ \therefore PR=4\end{array}$

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}GJ/MO=GL/MR\\ 9/6=8/OP\end{array}$

Applying means extremes product theorem, we get

  $\begin{array}{l}9*MR=48\\ \therefore MR=5.33\end{array}$