Geometry
Geometry
Level
3
In Triangle(ABC), D, E, and F are on the sides BC, CA, and AB respectively such that AD, BE, and CF are concurrent at G. Given that BD = 2CD, the area of Triangle(GEC) = a = 3, Triangle(GCD) = b = 4. Find the area of Triangle(ABC).
The answer is 30.
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1 solution
Given: BD:DC=2:1, Tr. GCD=4 Sq. Units & Tr. GEC=3 Sq. Units. We see that Tr. GBD=8 Sq. Units and EG:GB=3:12=1:4. Now apply Menelaus's Theorem to Tr. CBE with segment AGD as the transversal. (EG/GB) (BD/DC) (CA/AE)=1 whence we can infer that E is the midpoint of CA and thus Tr. ABC = 2(3+4+8) = 30 Sq. Units