Question

in the figure, $overline{pq}$ is parallel to $overline{rs}$. the length of $overline{rp}$ is 2 cm; the length of $overline{pt}$ is 18 cm; the length of $overline{qt}$ is 27 cm. what is the length of $overline{sq}$?
a. 63 cm
b. 9 cm
c. 54 cm
d. 3 cm

Explanation:

Step1: Apply similar - triangle property

Since \(PQ\parallel RS\), \(\triangle TPQ\sim\triangle TRS\). Then, \(\frac{RP}{PT}=\frac{SQ}{QT}\).

Step2: Substitute the given values

We know that \(RP = 2\mathrm{cm}\), \(PT=18\mathrm{cm}\), and \(QT = 27\mathrm{cm}\). Substituting into \(\frac{RP}{PT}=\frac{SQ}{QT}\), we get \(\frac{2}{18}=\frac{SQ}{27}\).

Step3: Solve for \(SQ\)

Cross - multiply: \(18\times SQ=2\times27\). Then \(SQ=\frac{2\times27}{18}\). Simplifying, \(SQ = 3\mathrm{cm}\).

Answer:

D. 3 cm