The perimeter of equilateral triangle abc is 81/3 centimeters, find the length of the radius and apothem.
the radius of equilateral triangle abc is
the apothem of equilateral triangle abc is

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle =

Thus from the diagram , Side

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus °

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

Thus ,apothem  OE= 13.5 cm

Now for radius,

We consider ΔOBE

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

-18 degrees is the answer : )