1. D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?
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By: anil on 05 May 2019 01.46 am
ADE & ABC are similar, let area of $$ riangle$$ ABC = x, that of DBCE = x-8 For similar triangles Ratio of sides = $$sqrt{ ext(ratio of areas)}$$ AB/AD = $$sqrt{ frac{area.ABC}{area.ADE}}$$ 7/2 = $$sqrt{ frac{x}{8}}$$ 49/4 = $$frac{x}{8}$$ x = 98 area of quadrilateral BDEC = ABC - ADE = x - 8 = 98 - 8 = 90 $$frac{ADE}{BDEC} = frac{8}{90} = frac{4}{45}$$ So the answer is option A.
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