Question

A lady wants to make an ope-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)

Answer 1

(11-2x)(14-2x) = 80

(11-2x)(7-x) = 40

77 - 25 x + 2 x^2 = 40

2 x^2 - 25 x + 37 = 0

x = [ 25 +/- sqrt(625 - 296) ]/4

= [ 25 +/- 18.1 ] / 4

= 10.7, too big for sheet
or
= 1.73 ok

check
11 - 2(1.73 ) = 7.55
14 - 2(1.73 ) = 10.55
7.55 * 10.55 = 79.65 close enough to 80