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In the figure (ii) given below, PQ ∥ AC, AP = 4 cm, PB = 6 cm and BC = 8 cm, find CQ and BQ.

In the figure (ii) given below, PQ ∥ AC, AP = 4 cm, PB = 6 cm and BC = 8 cm, find CQ and BQ. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

Considering △ABC and △PBQ,

∠B = ∠B (Common angle)
∠BPQ = ∠BAC (Corresponding angle are equal)

So, by AA rule of similarity △ABC ~ △PBQ.

∴BQBC=BPAB⇒BQ8=6AP+PB⇒BQ8=64+6⇒BQ=4810⇒BQ=4.8\therefore \dfrac{BQ}{BC} = \dfrac{BP}{AB} \\[1em] \Rightarrow \dfrac{BQ}{8} = \dfrac{6}{AP + PB} \\[1em] \Rightarrow \dfrac{BQ}{8} = \dfrac{6}{4 + 6} \\[1em] \Rightarrow BQ = \dfrac{48}{10} \\[1em] \Rightarrow BQ = 4.8

CQ = BC - BQ = 8 - 4.8 = 3.2 .

Hence, BQ = 4.8 cm and CQ = 3.2 cm.

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