SOLUTION: In △ABC, ​ DG=32 cm ​. What is the length of ADŻŻŻŻŻ? Enter your answer in the box. cm An acute triangle A B C is drawn. E is the midpoint of si

Algebra ->  Geometry-proofs -> SOLUTION: In △ABC, ​ DG=32 cm ​. What is the length of ADŻŻŻŻŻ? Enter your answer in the box. cm An acute triangle A B C is drawn. E is the midpoint of si      Log On


   

Question 1103741: In △ABC, ​ DG=32 cm ​.

What is the length of ADŻŻŻŻŻ?
Enter your answer in the box.
cm
An acute triangle A B C is drawn. E is the midpoint of side A C. Segment A E and segment C E are labeled with double tick mark. F is the midpoint of side A B. Segment A F and segment F B are labeled with single tick mark. D is the midpoint of side B C. Segment B D and segment C D are labeled with triple tick mark. Line segment A D and C F and B F are medians of the triangle. Medians intersect with each other at an interior point labeled as G.
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
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There is well known property of medians of a triangle: 

    In any triangle, medians are concurrent and their common intersection point 

    divides each median in proportion 2:1, counting the median parts from the vertex.



So, if DG = 32 cm,  then  AG = 64 cm, and the entire median AD is 32 + 64 = 96 cm.

Solved.

On the property of medians, see the leson
    - Medians of a triangle are concurrent
in this site.