Question

In the adjoining figure, line k || line l || line m. Their transversals, line c and line d, cut them at points X, Y, Z and P, Q, R respectively. If l (XY) = 5, l (YZ) = 3 and l (PQ) = 5.5, find l (QR).

Answer 1

Given: line k || line l || line m
Transversals line c and line d cut the lines at points X,Y,Z and P,Q,R respectively.
l(XY) = 5, l(YZ) = 3, l(PQ) = 5.5
According to the property of three parallel lines and their transversals,
$$\begin{gathered} \frac{l\left(\mathrm{XY}\right)}{l\left(\mathrm{YZ}\right)}=\frac{l\left(\mathrm{PQ}\right)}{l\left(\mathrm{QR}\right)} \\ \therefore \frac{5}{3}=\frac{5.5}{l\left(\mathrm{QR}\right)} \\ \therefore 5\times l\left(\mathrm{QR}\right)=3\times 5.5 \\ \therefore l\left(\mathrm{QR}\right)=\frac{3\times 5.5}{5}=3.3 \end{gathered}$$