I need help with geometry.
A certain square and a certain equilateral triangle have the same perimeter. The square and triangle are inscribed in circles, as shown below. If A is the area of the square and B is the area of the triangle, then find A/B.
Let the perimeter ==P
Then the side length of the square==P/4
Area of the square==(P/4)^2==P^2 / 16
Side length of the equilateral triangle==P/3
Area of the triangle ==1/2 * (P/3)^2 * sin(60)
==1/2 * P^2/9 * (sqrt(3/2)
==P^2 / [12 sqrt(3)]
Area A / B ==[P^2 / 16] / [P^2 / (12sqrt(3))]
==3 * sqrt(3) / 4
