Question

if the length of median of an equilateral triangle is x cm, then find its area.

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

Answer:

x²√3/3 cm

Step-by-step explanation:

Median in equilateral triangle is perpendicular bisector of the side.when side is a cm, then length of median will bex = √[(a)²-(a/2)²]   =√(3a²/4)  =(a/2)√3⇒x = (a/2)√3⇒a = 2x/√3now. area = (√3/4)a²                 = (√3/4)×(2x/√3)²                 = x²√3/3 cm