Question

In triangle abc pq||bc.if ap:pb=2:3 find the lengthier pq if bc=7.5cm

Answer 1

Answer:

If a line is drawn parallel to one side of a triangle to intersect the

other two sides in distinct points, the other two sides are divided in the same ratio.

As PQ∥BC

So  AP/PB  = AQ/QC

∠AQP=∠ACB

∠APQ=∠ABC

So by AAA △AQP∼△ACB

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Hence  

Area(APQ)/Area(ABC) =(AP)^2/(AB)^2

Area(ABC)/Area(APQ)=(AP)^2/(AP+PB)^2

Area(APQ)/Area(ABC)=(x)^2/(3x)^2

Area(APQ)/Area(ABC)=1/9

Let Area(APQ)=k

Area(ABC)=9k

Area(BPQC)=Area(ABC)−Area(APQ)=9k−k=8k

Area(APQ)/Area(BPQC)=1/8

∴ the ratio of the △APQ and trapezium BPQC = 1/8

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