SOLUTION: What is the ratio of the square's area to the circle's area if the square and circle have equal perimeter?
Algebra.Com
Question 237229: What is the ratio of the square's area to the circle's area if the square and circle have equal perimeter?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let r= radius of the circle, and let x = side of the square.
Perimeter of circle = .
Perimeter of rectangle =
If the perimeters are equal, then
You need to find the ratio of the area of the square to the area of the circle.
Area of circle =
Area of square =
Ratio of area of square to area of circle =
Before proceeding, just for fun (and it will be helpful later!!), find the ratio of using the equation above . Divide both sides by :
Divide out the 2 factor:
Divide both sides by 2, and multiply both sides by .
.
NOW:
RATIO of AREAS=
=
=
=
=
This is quite an interesting problem! You may want to get a second opinion on it!!
Dr. Robert J. Rapalje
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