Medians and Side Lengths

[Tahmid]

pls give me the solution of this problem:
Find the ratio of the area of a given tringle to that of a tringle whose sides have the same lengths as the medians of the original triangle.

[SANZEED]

pls give me the solution of this problem:
Find the ratio of the area of a given tringle to that of a tringle whose sides have the same lengths as the medians of the original triangle.

Let $ABC$ be the triangle and let $AD,BE,CF$ be its medians.Extend $FE$ to $M$ such that $FE=EM$.Join $A,M;C,M;D,M$.You can easily prove that $AMCF,BEMD,EMCD$ are parallelograms. Then $ADM$ is the triangle with side lengths equal to the medians. Now let $DM$ intersect $EC$ at $N$. Since $EMCD$ is a parallelogram, $N$ is the midpoint of $DM$ and $EC$. Thus $\frac {(ABC)}{(ADM)}=\frac {\frac{1}{2}(ABC)}{\frac{1}{2}(ADM)}$
$=\frac {(ADC)}{(ADN)}=\frac{AC}{AN}=\frac{4}{3}$

[Phlembac Adib Hasan]

pls give me the solution of this problem:
Find the ratio of the area of a given tringle to that of a tringle whose sides have the same lengths as the medians of the original triangle.

ছেলে, তোমার না Geometry Revisited শেষ করার কথা ছিল, করেছ? মনে তো হয় না। কারণ করলে এটা জিজ্ঞেস করার কথা না। Revisited-এর শেষে উপরের proof-টা দেয়া আছে।