Question

in triangle ABC, if DE║BC and DE:BC = 5:8 , Then find the ratios of areas trapezium BCED and triangle ABC.​

Answer 1

Answer:

According to question find the ratio of ar (Δ ADE) and ar (DECB).

Answer 2

Answer:

Given, DE ∥ BC. In ΔADE and ΔABC We know that, ∠ADE = ∠B [Corresponding angles] ∠DAE = ∠BAC [Common] Hence, ΔADE ~ ΔABC (AA Similarity) Since the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides, we have, Ar(ΔADE)Ar(ΔABC)Ar(ΔADE)Ar(ΔABC) = DE2BC2DE2BC2 Ar(ΔADE)Ar(ΔABC)Ar(ΔADE)Ar(ΔABC) = 32523252 Ar(ΔADE)Ar(ΔABC)Ar(ΔADE)Ar(ΔABC) = 925925 Assume that the area of ΔADE = 9 x sq units And, area of ΔABC = 25 x sq units So, Area of trapezium BCED = Area of ΔABC – Area of ΔADE = 25x – 9x = 16x Now, Ar(ΔADE)Ar(trapBCED)Ar(ΔADE)Ar(trapBCED) = 9x16x9x16x Ar(ΔADE)Ar(trapBCED)Ar(ΔADE)Ar(trapBCED) =9/16

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