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Math Help - finding the biggest posible rectangle inside a quadrilateral

  1. #1
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    finding the biggest posible rectangle inside a quadrilateral

    Hi (first time poster),

    This problem comes up at work from time to time. I'm hoping to find a simple technique for finding the answer.

    We construct various outdour sport surfaces, tennis courts running tracks...

    Every once in a while we get a slab of ashphalt in the form of a quadrilateral without any right angles and no parallel lines.. Our job is to find the biggest posible rectangle in the form width (x) length 2x inside this form. Is there a formula to find the placement of the rectangle?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Dolus View Post
    Hi (first time poster),

    This problem comes up at work from time to time. I'm hoping to find a simple technique for finding the answer.

    We construct various outdour sport surfaces, tennis courts running tracks...

    Every once in a while we get a slab of ashphalt in the form of a quadrilateral without any right angles and no parallel lines.. Our job is to find the biggest posible rectangle in the form width (x) length 2x inside this form. Is there a formula to find the placement of the rectangle?
    I cannot see how a formula can be derived with those. A biggest x by 2x rectangle inscribed, or even just inside, an irregular quadrilateral?
    The most you can do is by trial and error. Draw the quadrilateral on paper in scale. Make or cut some x by 2x rectangles. Play with them on the drawn quadrilateral until you find which x by 2x rectangle is the biggest to fit. Get that rectangle's dimensions by scale.
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