SOLUTION: Swore 360 inches long is cut into two pieces. One piece is formed into a square and the other into circle. If the two figures have the same area, What are the lengths of the two pi

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Question 987371: Swore 360 inches long is cut into two pieces. One piece is formed into a square and the other into circle. If the two figures have the same area, What are the lengths of the two pieces of wire ?
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A way to start this can be
Let p be perimeter of the square;
Let 2pi*r be the circumference of the circle;
p%2B2pi%2Ar=360.

p%2F4 would be the side length of the square, and area is %28p%2F4%29%5E2.

pi%2Ar%5E2 would be area of the circle.

This may be enough for you to continue on to figure the two lengths making up the original wire of length 360.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


When the wire is cut, the length of one piece will be the circumference of a circle of radius , which is to say . The length of the other piece will be the perimeter of a square of side length , which is to say . The measures of these two pieces sum to 360 inches according to the problem statement.

(1)

The area of the circle of radius is and the area of the square of side is . These two areas are equal according to the problem statement.

(2)

Solve the system for and . Then calculate and

John

My calculator said it, I believe it, that settles it