Size of Squares

[Guest]

A box is to be made from a sheet of material by removing squares from each corner and bending up remaining edges. Determine size of square removed so finished box has a length 3 times width.

Sheet of material: 12 in. * 16 in.

Volume of box: length * width * height.

X = side of square removed.

Not sure how to proceed.

[Guest]

Sheet of material: 12 in. * 16 in.

Volume of box: length * width * height.

X = side of square removed.

Yes OK so far, but you haven't started to proceed yet.
Set up equations describing the facts you are given and have established so far

[Guest]

12 * 16 = 192 sq. in. (Area of sheet)

L= 3W (Length of finished box 3 times width)


12 - 2X (Width minus 2 squares) 16 - 2X (Length minus 2 squares)

(16 - 2X) (12 - 2X)

192 - 32X - 24X + 4X^2 (FOIL)

192 - 56X + 4X^2 (Combining terms)

4X^2 - 56X + 192 (Rearranging)

Not sure.

[Guest]

This gives the area of the base of the box in terms of X.....you don't really need it for this question.


You wrote this down but didn't make use of it.??

L= 3W (Length of finished box 3 times width)


12 - 2X (Width minus 2 squares) 16 - 2X (Length minus 2 squares) ....Yes OK

(16 - 2X) (12 - 2X)....dont multiply them, you need to put the length bit equal to 3 times the width bit as an equation as you stated L = 3W and solve for X.

[Guest]

" you need to put the length bit equal to 3 times the width bit as an equation as you stated L = 3W and solve for X. "

(16 - 2X) = 3(12 - 2X)

16 - 2X = 36 - 6X

16 - 16 - 2X = 36 - 16 - 6X

-2X = 20 - 6X

-2X + 6X = 20 - 6X + 6X

4X = 20

4X / 4 = 20 / 4

X = 5

16 - 2(5) = 16 - 10 = 6 (Length of box)

12 - 2(5) = 12 - 10 = 2 (Width of box)

Length of box is 3 times width.

Correct ?

[Guest]

Yes, that's it now

[Guest]

Thanks.