Ratio of Area

Geometry Level 4

$ABC$ is a triangle, with $D$ and $E$ are the points on lines $AB$ and $BC$ , respectively.

Given that $BD:DA=1:2$ and $AE :EC=1:4$ .

Find the ratio of the area of triangle $DEF$ to that of triangle $BFC$ .

\frac3{25}

\frac2{15}

\frac4{25}

\frac1{10}

2 solutions

Niranjan Khanderia
Mar 28, 2020

WLOG let area ABC=1.
So area EDB=1/5 * 1/3.
Area DBC=1/3.
So Areas DBC - EDB=4/15.
So areas EDB/DBC should be something/15 * something.
So denominator most likely has to be 15.
From the selection, answer is 2/15,

Ahmad Saad
Jan 12, 2017

Ratio of Area

2 solutions

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