Tag: triangles

In the sides $BC,CA,AB$ of a triangle $ABC$, three points $D,E,F$ are taken such that each of $BD,CE,AE$ is equal to one-third of the corresponding side, then
$\triangle DEF=\dfrac {1}{2}\triangle ABC$.

In any triangle, medians meet at a point and divide each other as the ratio of $2:3$

If $AD$ and $PM$ are medians of triangles $ABC$ and $PQR$, respectivetly where $\triangle ABC \sim \triangle PQR$, then  $\dfrac {AB}{PR}=\dfrac {AC}{PM}$.

The area of two similar triangles are $200$ and $128$, then the ratio of their corresponding altitude is __________