SOLUTION: In a triangle, the lengths of three medians are 4, 5 and 6, find the area of the triangle.

SOLUTION: In a triangle, the lengths of three medians are 4, 5 and 6, find the area of the triangle.

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Question 251486: In a triangle, the lengths of three medians are 4, 5 and 6, find the area of the triangle.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
area of a triangle in terms of the median is expressed as follows:

The area of a triangle can be expressed in terms of the medians by:

where:

.

see http://mathworld.wolfram.com/TriangleMedian.html for details.

in terms of your problem:

m1 = 4
m2 = 5
m3 = 6

area of the triangle is therefore:

this becomes:

which becomes:

which becomes:

which becomes

A = 13.22875656

here's another reference:

http://www.math10.com/en/geometry/median.html

here's yet another.

http://pballew.net/medians.htm

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