Question

In the given figure, QR $∥$ CB and RP $∥$ AC. If BR = 10 cm, QA = 12 cm, BP = 12 cm and PC = 18 cm, then find the lengths of AR and QC.

Approach

Using Basic Proportionality Theorem twice, $\frac{BP}{PC} = \frac{BR}{R A}$ gives $\frac{12}{18} = \frac{10}{A R}$ , so $A R = 15$ cm. Similarly, $\frac{A R}{RB} = \frac{A Q}{QC}$ gives $\frac{15}{10} = \frac{12}{QC}$ , so $QC = 8$ cm.

Step-by-step working

1
PR $∥$ CA $\Rightarrow$ $\frac{BP}{PC} = \frac{BR}{R A}$ $\Rightarrow$ $\frac{12}{18} = \frac{10}{A R}$ $\Rightarrow$ AR = 15 cm
1 mark
2
QR $∥$ CB $\Rightarrow$ $\frac{A R}{RB} = \frac{A Q}{QC}$ $\Rightarrow$ $\frac{15}{10} = \frac{12}{QC}$ $\Rightarrow$ QC = 8 cm
1 mark

Concepts used

similar trianglesbasic proportionality theoremparallel lines

Approach

Step-by-step working

Concepts used

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