Question

Given RS||TU, RS=4, RQ=x+3, QT= 2x + 10, Find RQ and QT

Answer 1

Given that

`RS\parallel TU`

Given data

`\begin{gathered} RS=4 \\ RQ=x+3 \\ QT=2x+10 \\ UT=10 \end{gathered}`

Using the method of similar ratios

`(RS)/(RQ)=(UT)/(QT)`

Therefore,

`(4)/(x+3)=(10)/(2x+10)`

Cross-multiply

`\begin{gathered} 4(2x+10)=10(x+3) \\ 8x+40=10x+30 \end{gathered}`

Collect like terms

`\begin{gathered} 40-30=10x-8x \\ 10=2x \end{gathered}`

Divide both sides by 2

`\begin{gathered} (10)/(2)=(2x)/(2) \\ 5=x \\ \Rightarrow x=5 \end{gathered}`

Let us now solve for RQ and QT

`\begin{gathered} \text{RQ}=x+3=5+3=8 \\ QT=2x+10=2(5)+10=10+10=20 \end{gathered}`

Hence,

`\begin{gathered} RQ=8\text{units} \\ QT=20\text{units} \end{gathered}`