There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.
Answer:
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 =
![=[tex]81\sqrt{3}](https://tex.z-dn.net/?f=%3D%5Btex%5D81%5Csqrt%7B3%7D)

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