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

A.

26 cm

B.

52 cm

C.

75 cm

D.

100 cm

The correct answer is B. 52 cm

The apothem is the distance from which the altitudes of the triangle to one of its sides. It can be calculated through the equation below,

tan 30° = apothem / 0.5 (length of side)

Substituting the known values,

tan 30° = 5 / 0.5x

The value of x from the equation above is 17.32. Multiplying this value by 3 (because a triangle has 3 sides), we get an answer of 51.96 cm or approximately equal to 52. Thus, the answer is letter B.