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Math Help - word problem on quadratic equations

  1. #1
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    word problem on quadratic equations

    A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard. _____ Helping hints__ V= L.W.H where H (height) is 2 units. also L (length) and W (width) are 4 units less when the corners of rectangular are cut out.___ Plese help me anyone, after I tried without success. ____
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by mirdita59 View Post
    A rectangular piece of cardboard is 2 units longer than it is wide. From each of its corners a square piece 2 units on a side is cut out. The flaps are then turned up to form an open box that has a volume of 70 cubic units. Find the length and width of the original piece of cardboard. _____ Helping hints__ V= L.W.H where H (height) is 2 units. also L (length) and W (width) are 4 units less when the corners of rectangular are cut out.___ Plese help me anyone, after I tried without success. ____
    ok, you already have H=2.
    now, originally, you have L for length and L-2 for width..
    but since the 2x2 was cut on the corners, the new length would be L-4 and the new width would be (L-2)-4=L-6.
    a box is 70 cubic units = 2(L-4)(L-6) = 2(L^2 - 10L + 24)
    so, L^2 -10L + 24 - 35 = L^2 -10L - 11 = 0
    factoring, you would get (L - 11)(L + 1) = 0 --> L=11 or L= -1.
    since there is no negative distance, answer is L=11.
    so the width is 9.
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