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Math Help - The Wire - Areas of a Square & Circle Along a Wire?

  1. #1
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    The Wire - Areas of a Square & Circle Along a Wire?

    Hey guys, if there's any way one of you could point me in the right direction for this problem, I would greatly appreciate it.

    A wire 360 inches long is cut into two pieces. One piece is formed into a square and the other into a circle. If the resulting square circle have the same area, find the lengths of the two pieces of wire to the nearest tenth of an inch.

    Thanks in advance!
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: The Wire - Areas of a Square & Circle Along a Wire?

    You can set up an equation that equates the two areas based on the length of their perimeters. For a square if the perimeter is x then one side is length x/4, and the area is (x/4)^2. For a circle if the circumference is y then the radius is y/(2 pi) and the area is y^2/(4 pi). Set these two areas equal, and add in the condition that x + y = 360, and solve for x and y.
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    Senior Member MaxJasper's Avatar
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    Re: The Wire - Areas of a Square & Circle Along a Wire?

    Hint: 169.14
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