SOLUTION: The area of the rectangular piece of cardboard shown on the left is 171 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and tur

Algebra ->  Surface-area -> SOLUTION: The area of the rectangular piece of cardboard shown on the left is 171 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and tur      Log On


   

Question 602757: The area of the rectangular piece of cardboard shown on the left is 171 square inches. The cardboard is used to make an open box by cutting a 2 inch square from each corner and turning up the sides. If the box is to have a volume of 150 cubic inches, find the length and width of the cardboard that must be used.
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
assume that the rectangular piece of cardboard has length of L and width of W

L*W = 171
so L = 171/W

if the cardboard is cut 2 inch square each, the dimension of the box will be:
(L - 2*2)*(W - 2*2)*2 (length * width * height)

Volume of the box:
V = length * width * height
150+=+%28171%2FW+-+4%29%2A%28W+-+4%29%2A2
150%2F2+=+%28171%2FW+-+4%29%2A%28W+-+4%29
75+=+171+-+684%2FW+-+4W+%2B+16
(multiply all by W)
75W+=+171W+-+684+-4W%5E2+%2B+16W
4W%5E2+%2B+75W+-+171W+-+16W+%2B+684+=+0
4W%5E2+-+112W++%2B+684+=+0
(divide all by 4)
W%5E2+-+28W+%2B+171+=+0
%28W+-+9%29%2A%28W+-+19%29+=+0
W - 9 = 0 or W - 19 = 0
W = 9 or W = 19
L = 171/9 = 19 or L = 171/19 = 9


so, the length and width of the cardboard used are 19 inch and 9 inch