Open Box Problem

Question

A open top box is to be created from a piece of cardboard measuring  26 inches by 35 inches by cutting out identical squares with side length of x from each corner and folding up the sides. Express the surface area A of the box as a function of x

Answer 1

If you have a rectangle 26 x 35, but you remove x from each corner, your dimensions become:

26 - 2(x) width

35 - 2(x) length

Surface area are all sides (except the top in this case) so just add these together:

Front & Back = (2)(26 - 2x)

Left & Right = (2)(35 - 2x)

bottom = (26-2x)(35-2x)

A = (2)(26 - 2x) + (2)(35 - 2x) + (26-2x)(35-2x) then simplify.... (I'll leave that to you to do)

Answer 2

the bottom of the box is now (26-2x) by (35-2x)

The area of the bottom is (26-22)(35-2x)

the area of two opposite sides are

2x(26-2x) and 2x(32-2x)

add those 3 terms to get the total surface area:

(26-2x)(35-2x) + 2x(26-2x) + 2x(35-2x) = surface area = A

bottom area + 2 opposite sides' area + the other 2 sides' area

A = 910 -70x-52x +4x^2 +52x -4x^2 +70x -4x^2

A = 910-4x^2