Alady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11in. by 16 in. piece of cardboard as shown in the diagram. she figures that versatility the area of the bottom must be 80in^2. what size of square should be cut from each corner? (round three decimal places)

Let the size of the sides of the bottom of the box be x and y, and let the size of the sides of the square she cuts be z, then:
xy = 80 . . . (1)
2z + x = 11 => x = 11 - 2z . . . (2)
2z + y = 16 => y = 16 - 2z . . . (3)

Putting (2) and (3) in (1) gives
(11 - 2z)(16 - 2z) = 80
176 - 22z - 32z + 4z^2 = 80
4z^2 - 54z + 176 = 80
4z^2 - 54z + 96 = 0
z = 2.106

Therefore, the size of the sides of the square she cuts is 2.106 inches.