The area of a circle inscribed in an equilateral triangle is 154 square centimeters. What is the perimeter of the triangle? Use pi=22/7 and square root of 3= 1.73.

1 Answer
Jan 6, 2016

Perimeter =36.33 cm.

Explanation:

This is Geometry, so lets look at at a picture of what we are dealing with:
enter image source here

Acircle=πr2XXXXXXr=Aπ

We are told
XXXA=152cm2
and to use
XXXπ=227

r=7 (after some minor arithmetic)

If s is the length of one side of the equilateral triangle and t is half of s

XXXt=rcos(60)

XXXx=732

and
XXXs=2t=73

XXXx=12.11 (since we are told to use 3=1.73)

Perimeter =3s

XXXXXX=3×12.11=36.33