Open-top boxes are constructed by cutting equal squares from the corners of cardboard sheets that measure 32cm by 28cm. Determine...

The first step to solving this problem is to create the
equation.  The volume of any open-top box is the length times width times height.  Let
the dimensions of the square being cut out of each corner of the rectangular cardboard
be x by x.  The length of the formed box will be (32-2x). The width will be (28-2x). The
height will be x. The equation to solve
becomes:

V=(32-2x)(28-2x)x

1920=(32-2x)(28-2x)x,
or

(32-2x)(28-2x)x-1920=0

The
equation can be solved by finding the zeros, x-intercepts, on a
graph.

src="/jax/includes/tinymce/jscripts/tiny_mce/plugins/asciisvg/js/d.svg"
sscr="-10,20,-2000,100,2,200,1,2,200,300,200,func,(32-2x)(28-2x)x-1920,null,0,0,,,black,1,none"/>

The
graph shows that x=4, 6, or 20.

If x=4, then the length is
32-2(4)=24 cm, the width is 28-2(4)=20 cm and the height is 4
cm.

If x=6, then the length is 32-2(6)=20 cm, the width is
28-2(6)=16, cm and the height is 6 cm.

The value for x=20
is not possible since it would make the box edges negative.