A square and an equilateral triangle have the same perimeter. Let A be the area of the circle circumscribed about the square and B be the area of the circle cicumscribed about the triangle. Then A/B=?

1 Answer
Jul 29, 2018

Let the common perimeter be c
So each side of the square c/4
And the circumradius of the square (r_s)=1/2sqrt2xxc/4=c/(4sqrt2)

So the area of the circle circumscribed about the square will be

A=pir_s^2=pic^2/32

Each side of the triangle will be c/3

Its height h=sqrt3/2xxc/3

The circumradius of the triangle (r_t)=2/3xxsqrt3/2xxc/3=c/(3sqrt3)

So area of the circle cicumscribed about the triangle.

B=pir_t^2=pic^2/27

Hence the ratio A/B=27/32