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 : 4B. 9: 16C. 3: 5D. 9 : 25

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.

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.

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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