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.

Answer 1

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