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As shown in the diagram, BD/DC=2,CE/EA=3, and AF/FB=5. Find [DEF]/[ABC].

 

 Feb 22, 2022
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 \(\displaystyle \text{Let the area of the triangle ABC be }\; \Delta,\\ \text{then }\; \frac{1}{2}AB.AC.\sin A = \Delta.\\ \text{So, since }\;AF=5AB/6,\; \text{and}\;AE=AC/4,\\ \text{the area of the triangle AFE=}\;\frac{1}{2}.\frac{5}{6}AB.\frac{1}{4}AC. \sin A = \frac{5}{24}\Delta.\)

 

Over to you.

 Feb 23, 2022

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