Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle DMT is [ABC] = \(160\).

Guest Apr 30, 2022

#2**+2 **

Note that since AM is a median of triangle ABC, then BM = MC

And triangles ABM and ACM are equal because they are on equal bases with equal heighs

Looking at triangle ABM, ME and BD are medians and we can construct median AF in this triangle

These medians create 6 equal areas in the triangle

[ ABM ] = [ACM ] = (1/2)[ABC ] = 80

So

[ DMT ] = [ ABM ] / 6 = 80 / 6 = 40 / 3

CPhill Apr 30, 2022