A lady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 20 in. piece of cardboard as shown in the diagram. She figures that for versatility the area of the bottom must be 80 in. squared. What size of square should she cut from each corner?

Lets say she cuts squares of x by x in length.

Area of bottom will be (20 - 2x) (11 - 2x) = 80 inches squared

220 - 40x - 22x + 4x^2 = 80

4x^2 - 62x + 140 = 0

x^2 - 15.5x + 35 = 0

Using quadratic equation;

you get x = 2.743753901 0r 12.7562461 inches

The length of the square cannot be more than 11 inches

So the only squares you can cut are:

2.743753901 inches by 2.743753901 inches squares.