SOLUTION: can you help me solve this word problem; 1) A piece of cardboard has a length of 60cm and a width of 40cm. In order to make the cardboard into an open box, a box with no lid), a pi

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Question 204343: can you help me solve this word problem; 1) A piece of cardboard has a length of 60cm and a width of 40cm. In order to make the cardboard into an open box, a box with no lid), a piece of length x must be cut out of each corner.
-Write an equation to represent each dimension of the box.
-Using the dimensions from part a), find the S.A and Volume of the box. (Remember that it is an open box with no lid.)

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let L = the length of the finished box and W = is width. If h = its height, then: (The corners are assumed to be square with side = x)
L+=+60-2x
W+=+40-2x and...
h+=+x
The surface area, (4 sides plus bottom) SA (as a function of x), can be expressed as:
SA+=+2%28x%2860-2x%29%29%2B2%28x%2840-2x%29%29%2B%2860-2x%29%2840-2x%29 Simplify.
SA+=+%282%2860x-2x%5E2%29%29%2B%282%2840x-2x%5E2%29%29%2B%282400-200x%2B4x%5E2%29
SA+=+120x-4x%5E2%2B80x-4x%5E2%2B2400-200x%2B4x%5E2
highlight%28SA+=+-4x%5E2%2B2400%29
For the volume:
V+=+L%2AW%2Ah
V+=+%2860-2x%29%2840-2x%29%28x%29
V+=+%282400-200x%2B4x%5E2%29X
highlight_green%28V+=+4x%5E3-200x%5E2%2B2400x%29