Point $G$ is the midpoint of median $\overline{XM}$ of $ riangle XYZ$. Point $H$ is the midpoint of $\overline{XY}$, and point $T$ is the intersection of $\overline{HM}$ and $\overline{YG}$. Find the area of $ riangle MTG$ if $[XYZ] =150$.

Question

Point $G$ is the midpoint of median $\overline{XM}$ of $	riangle XYZ$. Point $H$ is the midpoint of $\overline{XY}$, and point $T$ is the intersection of $\overline{HM}$ and $\overline{YG}$. Find the area of $	riangle MTG$ if $[XYZ] =150$.

Yipploo · Accepted Answer

I doubt it's actually the AoPS team...Its $\boxed{25/2}$

PsyDAG · Answer

We would appreciate it if you could state the problem without all the dollar signs ($).

AoPS · Answer

We would really appreciate it if you could stop posting Homework Problems by AoPS on this website. Further activity may lead to a suspension of your account.

Point $G$ is the midpoint of median $\overline{XM}$ of $\triangle XYZ$. Point $H$ is the midpoint of $\overline{XY}$, and point $T$ is the intersection of $\overline{HM}$ and $\overline{YG}$. Find the area of $\triangle MTG$ if $[XYZ] =150$.