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Math Help - Rectangular box

  1. #1
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    Rectangular box

    A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
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  2. #2
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    Quote Originally Posted by sarahh View Post
    A rectangular box is to be made from a rectangular piece of shee metal 20in wide and 30in long by cutting a square piece of equal size from each of the corners and bending up the sides so that they make a 90 degree angle with the base. The base of the finished box will be 200 square inches. About how many inches high will the box be?
    Let x be the length of one side of one of the squares you have to cut off.

    Then you get:

    (20-2x)(30-2x) = 200 ......... Expand the brackets. You'll get aquadratic equation:

    4x^2-100x+400 = 0 ......... Solve this equation for x. Only one of the two solutions is valid with your problem.

    (For confirmation only: x = 5)
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    Why do we reject the 20 answer again?
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  4. #4
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    Quote Originally Posted by sarahh View Post
    Why do we reject the 20 answer again?
    Plug in the solution into the original equation:

    \begin{array}{ccc}(20-2 \cdot 20)(30-2 \cdot 20)& = &200\\\\ (-20)(-10)&=&200 \end{array}

    That means you cut off more than there exists. In my opinion quite impossible but the modern science ...
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  5. #5
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    Ahh that does make sense. Many thanks earboth!
    Sarah H.
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