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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.

 Apr 21, 2023
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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

 Apr 21, 2023

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