The medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at the centroid $G$. The line through $G$ that is parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If the area of triangle $ABC$ is 144, then find the area of triangle $ENG$.

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Mathematics

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27 July, 05:26

The medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at the centroid $G$. The line through $G$ that is parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If the area of triangle $ABC$ is 144, then find the area of triangle $ENG$.

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Aubrey Marshall · Answer 1

G divides each median in the ratio of 2 to 1 (the longer side goes from G to the angle) triangle AMN is similar to triangle ABC (why?) AMN is a scaled version of ABC (by a factor of ⅔) its area should be scaled by (⅔) ^2