*What is the area of a rectangle with perimeter of 80 units?*

If you try a few possible side lengths, you will find that there are many possible areas. For instance, if the rectangle is a square with side length 20 (note that the perimeter is 80), then the area is 400. If the length is 30 then the width is 10 and the area is 300, etc...

**Let x be the length of the rectangle.** Then the width is 40-x. (x+x+40-x+40-x=80).

**Then the area is given by x(40-x) or -x^2+40x. The bounds on x are 0<x<40, so the bound on the area is `0<a<=400` .**

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