Question

if the length of a median of an equilateral triangle is x centimetre 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 bex = √[(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