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Math Help - Dimensions of Original Cardboard

  1. #1
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    Dimensions of Original Cardboard

    A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 centimeters longer than it is wide. A square that measures 3 centimeters on a side is cut from each corner. When the
    sides are turned up to form the box, its volume is 765 cubic centimeters. Find the dimensions, in centimeters, of the original piece of cardboard.
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  2. #2
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    Hello, magentarita!

    This one takes a few diagrams ... or a good imagination.


    A rectangular piece of cardboard is to be formed into an uncovered box.
    The piece of cardboard is 2 cm longer than it is wide.
    A square that measures 3 cm on a side is cut from each corner.
    When the sides are turned up to form the box, its volume is 765 cm³.
    Find the dimensions, in centimeters, of the original piece of cardboard.

    Let W = width of cardboard.
    Then W+2 = length of cardboard.
    3-cm squares are removed from each corner.
    Code:
          : - - -  W+2  - - - :
        - *-------------------* -
        : |///:           :///| 3
        : | - * - - - - - * - | -
        : |   |           |   | :
        : |   |           |   | :
        W |   |           |   | W-6
        : |   |           |   | :
        : |   |           |   | :
        : | - * - - - - - * - | -
        : |///:           :///| 3
        - *-------------------* -
          : 3 :    W-4    : 3 :

    The sides are turned up to form an open-top box.
    Code:
             *-----------*
            /|          /|
           / |         / |3
          *-----------*  |
          |           |  *
         3|           | /
          |           |/ W-6
          *-----------*
               W-4

    We are told that the volume is 765 cm³.

    So we have: . (W-4)(W-6)3 \:=\:765


    Now solve for W.

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  3. #3
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    great............

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    This one takes a few diagrams ... or a good imagination.


    Let W = width of cardboard.
    Then W+2 = length of cardboard.
    3-cm squares are removed from each corner.
    Code:
          : - - -  W+2  - - - :
        - *-------------------* -
        : |///:           :///| 3
        : | - * - - - - - * - | -
        : |   |           |   | :
        : |   |           |   | :
        W |   |           |   | W-6
        : |   |           |   | :
        : |   |           |   | :
        : | - * - - - - - * - | -
        : |///:           :///| 3
        - *-------------------* -
          : 3 :    W-4    : 3 :
    The sides are turned up to form an open-top box.
    Code:
             *-----------*
            /|          /|
           / |         / |3
          *-----------*  |
          |           |  *
         3|           | /
          |           |/ W-6
          *-----------*
               W-4
    We are told that the volume is 765 cm³.

    So we have: . (W-4)(W-6)3 \:=\:765


    Now solve for W.
    Great pictures and set up. Tell me, how do you make those diagrams using a regular keyboard? Yes, I can now find w.
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  4. #4
    Super Member

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    Hello, magentarita!

    Tell me, how do you make those diagrams using a regular keyboard?

    I invented my own system a few years ago.


    First, I get into Code mode ... type [ code ] (without the spaces).

    Then I make a a few rows of "hyphen-space-hyphen-space..."
    Code:
    . . . - - - - - - - - - -
    . . . - - - - - - - - - -
    . . . - - - - - - - - - -

    Then I use COPY/PASTE to make more rows.

    Then I carefully plot out my points.
    I count very carefully, because the characters get out-of-line.

    It looks like this on my screen . . .

    . . . * - - - - - * - - - - -
    . . . | - - - -*- | - - - - -
    . . . | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . . * - - - - - * - - - -
    . . . - - - - - - - - - -


    But it looks like this in code mode.
    Code:
    . . . * - - - - - * - - - - -
    . . . | - - - -*- | - - - - -
    . . . | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . . * - - - - - * - - - -
    . . . - - - - - - - - - -

    If I add letters and numerals , it really gets out-of-line

    . . A * - - - - - * B - - - -
    . . . | - - - -*- | - - - - -
    . . 5 | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . D * - - - - - * C - - -
    . . . - - - 8 - - - - - -

    But it looks okay in code mode.
    Code:
    . . A * - - - - - * B - - - -
    . . . | - - - -*- | - - - - -
    . . 5 | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . D * - - - - - * C - - -
    . . . - - - 8 - - - - - -

    Then I remove the hyphens from the right end.
    (Use Delete or Backspace.)
    Code:
    . . A * - - - - - * B
    . . . | - - - -*- |
    . . 5 | - - * - - |
    . . . | -*- - - - |
    . . D * - - - - - * C
    . . . - - - 8

    Then I replace the other hyphens with spaces.
    Code:
        A * - - - - - * B
          |        *  |
        5 |     *     |
          |  *        |
        D * - - - - - * C
                8

    Yes, it's a lot of extra work, but I enjoy it.

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  5. #5
    MHF Contributor
    Joined
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    From
    NYC
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    great but...

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!


    I invented my own system a few years ago.


    First, I get into Code mode ... type [ code ] (without the spaces).

    Then I make a a few rows of "hyphen-space-hyphen-space..."
    Code:
    . . . - - - - - - - - - -
    . . . - - - - - - - - - -
    . . . - - - - - - - - - -
    Then I use COPY/PASTE to make more rows.

    Then I carefully plot out my points.
    I count very carefully, because the characters get out-of-line.

    It looks like this on my screen . . .

    . . . * - - - - - * - - - - -
    . . . | - - - -*- | - - - - -
    . . . | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . . * - - - - - * - - - -
    . . . - - - - - - - - - -


    But it looks like this in code mode.
    Code:
    . . . * - - - - - * - - - - -
    . . . | - - - -*- | - - - - -
    . . . | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . . * - - - - - * - - - -
    . . . - - - - - - - - - -
    If I add letters and numerals , it really gets out-of-line

    . . A * - - - - - * B - - - -
    . . . | - - - -*- | - - - - -
    . . 5 | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . D * - - - - - * C - - -
    . . . - - - 8 - - - - - -

    But it looks okay in code mode.
    Code:
    . . A * - - - - - * B - - - -
    . . . | - - - -*- | - - - - -
    . . 5 | - - * - - | - - - - -
    . . . | -*- - - - | - - - - -
    . . D * - - - - - * C - - -
    . . . - - - 8 - - - - - -
    Then I remove the hyphens from the right end.
    (Use Delete or Backspace.)
    Code:
    . . A * - - - - - * B
    . . . | - - - -*- |
    . . 5 | - - * - - |
    . . . | -*- - - - |
    . . D * - - - - - * C
    . . . - - - 8
    Then I replace the other hyphens with spaces.
    Code:
        A * - - - - - * B
          |        *  |
        5 |     *     |
          |  *        |
        D * - - - - - * C
                8
    Yes, it's a lot of extra work, but I enjoy it.
    Great but there's got to be an easier way.
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