Question

If OP = 14, SQ = 7, and QR = 24, find PR.

Answer 1

Given that

`\begin{gathered} OP=14 \\ SQ=7 \\ QR=24 \\ PR=\text{?} \end{gathered}`

Using the method of the ratio of similar figures,

Which says

`(OP)/(SQ)=(PR)/(QR)`

Therefore,

`(14)/(7)=(PR)/(24)`

Solving for PR

First of all, we will cross-multiply

`\begin{gathered} 7* PR=14*24 \\ 7PR=14*24 \end{gathered}`

Then, we will divide both sides by 7

`\begin{gathered} (7PR)/(7)=(14*24)/(7) \\ PR=2*24=48 \\ \therefore PR=48 \end{gathered}`

Hence,

`PR=48\text{units}`