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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] = \(160\).

 Apr 30, 2022
 #1
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The area of triangle DMT is 50.

 Apr 30, 2022
 #2
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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  

 

 

cool cool cool

 Apr 30, 2022

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