Question

.Line PQis such that P and Q are points on sides AB and AC respectivelyof ∆ABC. If AP=1cm, PB=3 cm, AQ = 1.5 cm and QC = 4.5 cm, prove that the ar(APQ)=1/16 ar(ABC)

Answer 1

Answer:

Given : In ΔABC, PQ is a line segment intersecting AB at P and AC at Q. AP = 1 cm , PB = 3cm, AQ= 1.5 cm and QC= 4.5cm.

In ∆APQ and ∆ABC,

∠A = ∠A [Common]

AP/AB = AQ/AC [Each equal to 1/4]

∆APQ ~ ∆ABC [By SAS similarity]

We know that the ratio of the two similar triangles is equal to the ratio of the squares of their corresponding sides

ar∆APQ /ar∆ABC = (AP/AB)²

ar∆APQ /ar∆ABC = ( ¼)²

ar∆APQ /ar∆ABC = 1/16

ar∆APQ = 1/16 × ar∆ABC

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