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Question
In ∆ABC, P and Q are points on sides AB and AC respectively such that PQ || BC. If AP = 4 cm, PB = 6 cm and PQ = 3 cm, determine BC.
Solution
In triangle ABC, P and Q are points on sides AB and AC respectively such that `PQ|| BC`.
In ΔAPQ and ΔABC,
Substituting value AP = 3cm,AB=10cm and PQ = 3cm, we get
`(AP)/(AB)=(3)/(BC)`
By cross multiplication we get
`4 xx BC = 3xx10`
`BC = (3xx10)/4`
`BC = 30/4`
`BC = 7.5 cm`
Hence, the value of BC is 7.5 cm.
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