Question

If the length of median of equilateral triangle is x cm ,then its area is?

Answer 1

Median in equilateral triangle is perpendicular bisector of the side.

when side is a cm, then length of median will be

x = √[(a)²-(a/2)²] 

 =√(3a²/4)

 =(a/2)√3

⇒x = (a/2)√3

⇒a = 2x/√3

now. area = (√3/4)a²

                = (√3/4)×(2x/√3)²

                = x²/√3 cm²

Answer 2

Median in equilateral triangle is perpendicular bisector of the side.

when side is a cm, then length of median will be

x = √[(a)²-(a/2)²] 

 =√(3a²/4)

 =(a/2)√3

⇒x = (a/2)√3

⇒a = 2x/√3

so, area = (√3/4)a²

                = (√3/4)×(2x/√3)²

                = x²/√3 cm