If P divides seg AB in ratio AP : PB = 2 : 1 , then PB is ____ part of AB.
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8th
Maths
Mensuration
Area of Trapezium
In ABC, P divides the sid...
MATHS
In △ ABC, P divides the side AB such that AP:PB = 1 : 2. Q is a point in AC such PQ∥BC. Find the ratio of the area of △ APQ and trapezium BPQC.
December 27, 2019avatar
Tanish Thakur
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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
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)
.plede mark brainlist answer
=
(AP+PB)
2
(AP)
2
Area(ABC)
Area(APQ)
=
(3x)
2
(x)
2
Area(ABC)
Area(APQ)
=
9
1
Let Area(APQ)=k
Area(ABC)=9k
Area(BPQC)=Area(ABC)−Area(APQ)=9k−k=8k
Area(BPQC)
Area(APQ)
=
8
1
∴ the ratio of the △APQ and trapezium BPQC =
8
1
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