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 circumscribed about the triangle. What pwecent of B is A? Solution Let us assume that the square has side length 1. Thelength of the diagonal of the square equals the diameter of thecircle circumscribed about it. This is (2). Sothe radius is (2)/2, and the area of circle isA=/2. Since the square has side length 1, then its perimeter is4. So each side of the triangle is length 4/3. Then theradius of the circle circumscribed about is is 43/9. So the area of circle B=48/81. So B is 118.5% of A..

1. 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 circumscribed about the triangle.
What pwecent of B is A?
Solution
Let us assume that the square has side length 1. Thelength of the diagonal of the square equals
the diameter of thecircle circumscribed about it. This is (2). Sothe radius is (2)/2, and the area of
circle isA=/2.
Since the square has side length 1, then its perimeter is4. So each side of the triangle is length
4/3. Then theradius of the circle circumscribed about is is 43/9. So the area of circle B=48/81.
So B is 118.5% of A.