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

Given $QR ∥ CB$ and $RP ∥ A C$ in $△ A BC$ . By BPT, $\frac{BR}{A R} = \frac{BP}{PC}$ and $\frac{A R}{BR} = \frac{A Q}{QC}$ . Given $BR = 10, Q A = 12, BP = 12, PC = 18$ . From first ratio, $\frac{10}{A R} = \frac{12}{18} \Rightarrow A R = 15$ cm. From second ratio, $\frac{15}{10} = \frac{12}{QC} \Rightarrow QC = 8$ cm.

Step-by-step working

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

Concepts used

basic proportionality theoremparallel linestrianglefind length

Approach

Step-by-step working

Concepts used

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