Question

question 42 of 45 in the figure, pq is parallel to rs. the length of pq is 2 cm; the length of rs is 6 cm; the length of qt is 4 cm. what is the length of ts?

Explanation:

Step1: Identify similar triangles

Since $PQ\parallel RS$, $\triangle TPQ\sim\triangle TRS$.

Step2: Set up proportion

For similar triangles, $\frac{PQ}{RS}=\frac{TQ}{TS}$. Let $TS = x$. We know $PQ = 2$, $RS=6$ and $TQ = 4$. So $\frac{2}{6}=\frac{4}{x}$.

Step3: Cross - multiply and solve

Cross - multiplying gives $2x=4\times6$, so $2x = 24$. Then $x=\frac{24}{2}=12$.

Answer:

A. 12 cm