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 =
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
