help this is a math sos?

Question

a open bod is to be constructed from a rectangular piece of cardboard which measures 18 inches by 20 inches to make the box a square shaped cut is made at each corner of the rectangle and the sides folded up. Each square cut must be a whole number of inches on each side

a open *box

Answer 1

Let x = length of corner cut into length of the rectangle (20")
Let y = length of corner cut into width of the rectangle (18")

To make a square base, you need to have :
Length = Width
that is,
20 - 2x = 18 - 2y

Divide through by 2 :
10 - x = 9 - y

Solve for x :
x = y + 1

For example, if y = 1 inch, then x = 2 inches
and you'll have a square base of side 16 inches.

If y = 2 inches, then x = 3 inches
and the square base will have side = 14 inches.

If y = 3 inches, then x = 4 inches, side of square = 12 inches.

See how far you can go with this.

Answer 2

What's the question/objective?

If, for example, you cut a square 3in x 3in from each corner and folded up the sides, you would have a box that was 12 inches by 14 inches by 3 inches.

Answer 3

There is something missing from your question, as there are many possible answers. For example:

Cutting 1" squares from each corner will result in a box that is 16" x 18" x 1"; 2" results in 14" x 16" x 2"; etc.

Answer 4

Any square 1" -> 8" would make a box, let's assume you want one with maximum volume:

Volume = x * (18 - 2x) * (20 - 2x) = 360x - 76x^2 + 4x^3

It will be a maximum when its derivative vanishes:

d Volume / dx = 360 - 152x + 12x^2 = 0

90 - 38x + 3x^2 = 0

x = 38 +/- sqrt(38^2 - 4 * 3 * 90) / (2 * 3)

The closest integer x is 3. The other root, about 9.5" is too big.