Question

In triangle ABC, AE=DE=DC. If the area of triangle BEC is 48, what is the area of ABC?
a) 80. b)78
c) 72. c)68

Answer 1

Given :- In triangle ABC, AE=DE=DC. If the area of triangle BEC is 48, what is the area of ABC ?

a) 80

b)78

c) 72.

c)68

Solution :-

since, AE=DE=DC .

so,

→ BD = DE

now,

→ Area(∆ACE)/Area(BEC) = AE/BC = AE/(BD + DC) = AE/(DE + DE) = AE/2AE = (1/2) .

so,

→ Area(∆ACE)/48 = 1/2

→ Area(∆ACE) = 24 .

then,

→ Area(∆ABC) = Area(BEC) + Area(∆ACE) = 48 + 24 = 72 (C) (Ans.)

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