SOLUTION: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27√3 cm2. What is the side lenght AB, in cm?

Question 1105588: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27√3 cm2. What is the side lenght AB, in cm?

Found 2 solutions by KMST, greenestamps:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

An equilateral triangle with side length has a height
,
and an area ,
so if represents the length of side AB in cm, is the area of ABC in .

The altitude of an equilateral triangle is also a median,
so it splits the triangle into two triangles with the same area.
Those triangles are ABD and ACD, each with an area equal to {1/2}}} of the area of ABC.
Triangle ABD is similarly split into triangles ABE and AED,
each with area equal to of the area of ABD,
meaning of the area of ABC.
Triangle ARC is the union of triangles ABD and AED,
so its area is of the area of ABC.
That is
.

.
The length of side AB is .
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The altitude of an equilateral triangle is also a median. If AE is a median of triangle ABD, then the base of triangle AEC is 3/4 the side length of the equilateral triangle.

If the area of triangle AEC is , then the area of the equilateral triangle is 4/3 of that, or .

The area of an equilateral triangle is , so

The side length of the equilateral triangle is 12 cm.
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SOLUTION: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27&#8730;3 cm2. What is the side lenght AB, in cm?

SOLUTION: Equilateral triangle ABC has altitude AD. Median AE of triangle ABD is drawn. If the area of triangle AEC is 27√3 cm2. What is the side lenght AB, in cm?