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jmc

prealgebra senior

Problem

The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fraction in terms of .
Solution
Let be the side length of the square and the radius of the circle. We are given and asked to find . Squaring both sides of the equation we obtain . We divide by to find .
Final answer
\frac{\pi}{4}