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

$\frac{RS}{RQ}=\frac{UT}{QT}$

Therefore,

$\frac{4}{x+3}=\frac{10}{2x+10}$

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

$\begin{gathered} \frac{10}{2}=\frac{2x}{2} \\ 5=x \\ \Rightarrow x=5 \end{gathered}$

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,

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