Question

In the figure, PQ is parallel to RS. The length of RP is 5cm; the length of PT is 30cm; the length of QT is 60cm. What is the length of SQ?○A.10cm○B.6cm○C.2cm○D.20cm

Answer 1

The triangles PTQ and RTS are similar; so the ratios of corresponding sides are equal.

Let us denote the unknown length SQ as x.

We could make the following similarity relation;

`\begin{gathered} (30)/(30+5)=(60)/(60+x) \\ \end{gathered}`

Cross multiply to obtain;

`\begin{gathered} 30(60+x)=60(35) \\ 1800+30x=2100 \\ \text{collect like terms} \\ 30x=2100-1800 \\ 30x=300 \\ \text{divide both sides by 30} \\ (30x)/(30)=(300)/(30) \end{gathered}`

Therefore;

Therefore, the answer is option A