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;

$\begin{gathered} \frac{30}{30+5}=\frac{60}{60+x} \\ \end{gathered}$

Cross multiply to obtain;

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

Therefore;

$x=10\operatorname{cm}$

Therefore, the answer is option A