An equilateral triangle has an apothem of 5 cm. Find the perimeter of the triangle to the nearest centimeter.

Answer 1

All of the angles are equal: A = B = C = 180/3 = 60o.

All of the sides are equal: a = b = c.

h = 5 cm, sin60 = h/a = 5/a, a = 5/sin60 = 5.77 cm.

P = a + b + c = 5.77 + 5.77 + 5.77 = 17 cm.

Answer 2

Correction: apothem = s/2*Tan(180/n).
5 = S/2*Tan(180/3), S = 17.32 cm.

P = 17.32 + 17.32 + 17.32 = 52 cm.