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?

Algebra ->  Triangles -> 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?      Log On


   

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(52887) About Me  (Show Source):
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Since the length of EC is  3%2F4  of the length of AD,  the area of the triangle AEC is  3%2F4  of the area of the triangle ABC.


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


    a%5E2%2A%28sqrt%283%29%2F4%29 = 36%2Asqrt%283%29.


Then  a%5E2 = 36*4;  hence,  a = 6*2 = 12 centimeters.    ANSWER

Solved.