Thread: 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?

Originally Posted by Dolus

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.