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Question
A line PQ is drawn parallel to the side BC of ΔABC which cuts side AB at P and side AC at Q. If AB = 9.0 cm, CA = 6.0 cm and AQ = 4.2 cm, find the length of AP.
Solution
In ΔAPQ and ΔABC,
∠APQ = ∠ABC ...(Since PQ || BC, so the angles are corresponding angles)
∠PAQ = ∠BAC ...(Common angle)
ΔAPQ ∼ ΔABC ...(AA criterion for similarity)
`=> (AP)/(AB) = (AQ)/(AC)`
`=> (AP)/9 = 4.2/6`
`=> AP = (4.2 xx 9)/6`
`=>` AP = 6.3 cm
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