Question

sq. units. In A ABC, points Pand Q are on sides AB and AC respectively such that PQ|| BC. If AP: PB =1:2 and ar(APQ) = 6 sq. units, then ar(PBCQ) = (a) 12 (b) 18 (c) 36 (d) 48​

Answer 1

Step-by-step explanation:

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

PB

AP

=

QC

AQ

∠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(ABC)

Area(APQ)

=

(AB)

2

(AP)

2

Area(ABC)

Area(APQ)

=

(AP+PB)

2

(AP)

2

Area(ABC)

Area(APQ)

= (3x) 2 (x) 2

Area(ABC)

Area(APQ)

= 91

Let Area(APQ)=k

Area(ABC)=9k

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

Area(BPQC)

Area(APQ)

= 81

∴ the ratio of the △APQ and trapezium BPQC = 81