If the length of a median of an equilateral triangle is x cm,then find its area ?
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Suppose,one side of triangle is y.
so, the base is also y . You all know median is bisect a line .
so one part of this side is y/2.
By pythogorus theorem,
Hypotonus2 = Height2 + Base2
y2 = x2 + (y/2)2
x2 = y2 - y2/4
x2 = 3y2/4
y2 = 4x2/3
y = 2x/root3
So, one side is 2x/root3
Area of equilateral triangle is = root3/4
Area = root3/4*2x/root3*2x/root3
= x2/root3 Ans