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 13.5 cm 27 cm 81 cm

OB = radius =27 cm

Apothem of equilateral triangle ABC is 13.5 cm.

Step-by-step explanation:

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

Perimeter of equilateral triangle =

Let the side be x

So,  

Refer the attached figure .

Since BC = 27√3 cm

BE = half of BC =

All angles of equilateral triangle is 60°

OB is the angle bisector

So, ∠OBC = 30°

In ΔOBE

The apothem is equivalent to the line segment from the midpoint of a side to any of the triangle's centers

So, OE is apothem

Thus The apothem of equilateral triangle ABC is 13.5 cm.

Now In ΔOBE

So, OB = radius =27 cm