Precalculus word problem

Question

A rectangular piece of cardboard measuring 12 inches by 18 inches is to be made into a box w/ an open top by cutting equal-sized squares from each corner and folding up the sides. Let x represent the length of a side of each such square in inches.

Answer 1

Calculate the amount of area you have to work with

Since a Box has all equal sides(or faces) and this will be an open box calculate the number of sides

Use this information versus the area you have to work with.

12 inches by 18 inches

12 x 18 = 216 square inches of card board area to work with

If you want one large opened top box with a total surface area of 216 square inches

The surface area of box is 6s² because all the sides are equal on each face.

But you need an opened box so the surface area will be 5s² because there is no top (6s² - 1s²)

You could try the following:

216 = 5s²

Divide both sides by 5

43.2 = s²

Get the square root of 43.2 to find s

√43.2 = s

6.572 = s

You can check by keeping in mind that your box has one bottom, four sides, and NO TOP so the surface area is for one large box.

5s²

5*(6.572)² = 5*43.19 = 215.95 square inches

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