Question

If the length of a median of equilateral triangle is x cm ,then find the area of triangle.

Answer 1

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