# Problem of the Week Problem C Three Perimeters

A median is a line segment drawn from the vertex of a triangle to the midpoint of the opposite side.

In $$\triangle DEF$$, a median is drawn from vertex $$D$$, meeting side $$EF$$ at point $$M$$.

The perimeter of $$\triangle DEF$$ is $$24$$. The perimeter of $$\triangle DEM$$ is $$18$$. The perimeter $$\triangle DFM$$ is $$16$$. Determine the length of the median $$DM$$.

Themes: Algebra, Geometry & Measurement