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If P divides seg AB in ratio AP : PB = 2 : 1 , then PB is ____ part of AB. |
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Answer» Answer: Type your QUESTION... 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 SHARE 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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