Q. 215.0( 1 Vote )

In a , point D is on side AB and point E is on side AC, such that BCED is a trapezium. If DE : BC = 3 : 5, then Area (): Area (âBCED) =
A. 3 : 4

B. 9: 16

C. 3: 5

D. 9 : 25

Answer :

Given in ΔABC, point D is on side AB and point E is on side AC, such that BCED is a trapezium and DE: BC = 3: 5.



In ΔABC and ΔADE,


ABC = ADE [corresponding angles]


ACB = AED [corresponding angles]


A = A [common angle]


We know that AAA similarity criterion states that in two triangles, if corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.


ΔABC ~ ΔADE


We know that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.



Let ar (ΔADE) = 9x sq. units and ar (ΔABC) = 25x sq. units


ar (trap BCED) = ar (ΔABC) – ar (ΔADE)


= 25x – 9x


= 16x sq. units


Now,



ar (ΔADE): ar (trap BCED) = 9: 16

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