Question

Find the area of an equilateral triangle, if the altitude is 5

Answer 1

If side is a cm, then length of altitude will be
x = √[(a)²-(a/2)²] 
  =√(3a²/4)
  =(a/2)√3
⇒x = (a/2)√3
⇒a = 2x/√3 = 10/√3

Now, area = (√3/4)a²
                 =(√3/4)×(10/√3)²
                 = 25/√3 cm²