SOLUTION: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27 sqrt3 cm^2, what is the side length AB, in cm?

Question 1151096: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27 sqrt3 cm^2, what is the side length AB, in cm?
Answer by ikleyn(52915) (Show Source): You can put this solution on YOUR website!
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Since the length of EC is    of the length of AD,  the area of the triangle AEC is    of the area of the triangle ABC.


Thus the area of the triangle ABC  is  {{36*sqrt(3)}}}  cm^2,  or


     = .


Then   = 36*4;  hence,  a = 6*2 = 12 centimeters.    ANSWER

Solved.

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