Find the length and width?

Question

A machine produces open boxes using square sheets of metal. The machine cuts equal sized squares measuring 3 inches on a side from corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 75 cubic inches, find the length and width of the open box

Answer 1

If you start with a square sheet, and remove 3" squares from each corner...

Volume=length x width x height.

So, you know the height of the box will be 3", once the sides are folded up, and the width will be the same on all four sides.

3(x)(x)= 75

75/3=25

(x)(x)=25

The solution would be that the length 5 inches and the height 3 inches.

Answer 2

the height of the box is 3 because of the squares cut from the side, so the area of the base of the box has to be 75/3=25
the original sheet of metal is a square, so the box will be too. the square has to have area 25, so the length and width are both 5

Answer 3

Simple, find the base factors of this numbers of 75. You now you need a 3cm in it somewhere so one side is going to equal 3cm. So divide 75 by 3 and get 25. The only whole intergers that divide into 25 apart from 1 and 25 are 5 and 5.

so the dimensions of the box are 3 x 5 x 5

Answer 4

Since you're starting from a square sheet, the length will be equal to the width.

Volume = L² X 3 = 75

L² = 25

L = 5
W = 5

Answer 5

let x be the size of the metal sheet

(x-6)^2 * 3 = 75
(x-6)^2 = 25
x-6 = 5
x = 11
so the box is 5x5x3

Answer 6

5"x5"x3"=75 cubic inches...Did I win?! :D

I hate story problems...