Question

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

Answer 1

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.