Question

I have a piece of cardboard that is twice as long as it is wide. If I cut a 2 inch by 2 inch square from each corner and fold up the resulting flaps, I get a box with a volume of 32 cubic inches. What are the dimensions of the cardboard with a detailed explanation?

Answer 1

looking for a little more help than that if possible xD

Answer 2

The dotted lines are the lines you fold up to create teh sides.
The width of the cardboard is w. After folding the sides up, the width of the box will be w - 4. The length of the cardboard is 2w. After folding up the sides, the length of the box will be 2w - 4. The height of the box is 2.
The volume of the box is
V = Length x width x height (of the box)
V = (2w - 4)(w - 4)(2) = 32

Answer 3

Alright, I was able to get there on my own. I get stuck at this part though.

Answer 4

Solve the equation:
Divide both sides by 2:
(2w - 4)(w - 4) = 16

Answer 5

Factor 2 out of first factor
2(w - 2)(w - 4) = 16

Answer 6

alright, then?

Answer 7

Divide both sides by 2
(w - 2)(w - 4) =8

Answer 8

Multiply out left side (using FOIL)
w^2 -4w - 2w +8 = 8

Answer 9

subtract 8 from both sides and collect like terms on left
w^2 - 6w = 0

Answer 10

so it's 0,6 in the end, and 6 times 2 is 12? so 6,12?

Answer 11

factor left side
w(w - 6) = 0
w = 0 or w - 6 = 0
w = 0 or w = 6
w = 0 is a meaningless solution for our problem, so discard it.
Now take w = 6, then L = 2w = 12
The cardboard measured 12 inches by 6 inches.

Answer 12

ah, thank you ^^

Answer 13

To check, since the cardboard is 12 x 6, the box is 8 by 2 and 2 inches tall, so 8 x 2 x 2 = 32, the correct volume of the box.