figuring a square

Question

i have a circle that is 100 feet around how big a square would fit in this circle

Answer 1

C=(pi)*d

100=(3.14159)*d

100/(3.14159)=d

31.831=d, the diameter

the diameter is the diagonal of the square and also the hypotenuse of an isosceles right triangle

now find the side of the square using the Pythagorean Theorem

x²+x²=31.831²

2x²=1013.212

x²=1013.212/2

x²=506.6 (this is the area of the square in square feet)

x=22.5077 feet

the biggest square is a 22.5077 by 22.5077 square whose area is 22.5077²=506.5965≈506.6 square feet which is what we got above