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Math Help - constructing wire frames

  1. #1
    Member Jonboy's Avatar
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    constructing wire frames

    Hello I just want to verify this answer:

    Two square wire frames are to be constructed from a piece of wire 100 inches long. If the area enclosed by one frame is to be one-half the area enclosed by the others, find the dimensions of each frame. (Disregard the thickness of the wire)

    So each sides on the square of smaller area is x
    Each sides on the be bigger square would have to be x\sqrt{2}

    Then I would do: 4x\,+\,4x\sqrt{2}\,=\,100

    x(4\,+\,4\sqrt{2})\,=\,100

    x\,=\,25\,+\,25\sqrt{2}

    Is this fundamentally sound answer? Thanks all.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jonboy View Post
    Hello I just want to verify this answer:

    Two square wire frames are to be constructed from a piece of wire 100 inches long. If the area enclosed by one frame is to be one-half the area enclosed by the others, find the dimensions of each frame. (Disregard the thickness of the wire)

    So each sides on the square of smaller area is x
    Each sides on the be bigger square would have to be x\sqrt{2}

    Then I would do: 4x\,+\,4x\sqrt{2}\,=\,100

    x(4\,+\,4\sqrt{2})\,=\,100

    x\,=\,25\,+\,25\sqrt{2}

    Is this fundamentally sound answer? Thanks all.
    The method is correct, your solution is wrong.
    4x + 4x \sqrt{2}= 100

    4x(1 + \sqrt{2}) = 100

    x = 25 \cdot \frac{1}{1 + \sqrt{2}}

    x = 25 \cdot \frac{1}{1 + \sqrt{2}} \cdot \frac{1 - \sqrt{2}}{1 - \sqrt{2}}

    x = 25 \cdot \frac{1 - \sqrt{2}}{1 - 2}

    x = 25(\sqrt{2} - 1)

    x = 25 \sqrt{2} - 25

    -Dan
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  3. #3
    Member Jonboy's Avatar
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    Thanks Topsquark, I completely understand now.
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