Question

What would be the height of an equilateral triangle whose perimeter is 60cm.

Answer 1

since it is a equilateral triangle so all the sides are equal.
Given: perimeter=60cm
To find: height of the triangle
Proof: by heron's formula
          semi perimeter= 60/2=30
           let the sides be a+a+a=60
            3a=60
            a=20
            by Heron's formula
          root s(s-a)(s-b)(s-c)
          root 30 (30-20)(30-20)(30-20)
          root 30 *10*10*10
          10*10 root 3
           =100 root 3:AREA
area of triangle = 1/2 *b*h
       100 root3   = 1/2*a/2*h
              ''           = 1/2 *20/2 *h
             '''             =1/2*10*h
              ''           = 1*5*h
        = 50 root 3