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Math Help - How many rectangles make up the new dimension (551)

  1. #1
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    How many rectangles (551) thanks to ticbol!

    The pattern below is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed?

    Can you please explain why? Thank you in advance.
    Attached Thumbnails Attached Thumbnails How many rectangles make up the new dimension (551)-pg-550.jpg  
    Last edited by fabxx; September 23rd 2008 at 04:48 AM.
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  2. #2
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    Quote Originally Posted by fabxx View Post
    The pattern below is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed?

    Can you please explain why? Thank you so much!
    The text is vague, and the diagram is, ah, confusing.
    So for me to solve your question, I will follow exactly what is in the text but I will alter the diagram a bit to get to a diagram that might solve the problem.

    The diagram:
    The L and W at the top of the pattern need to be re-drawn to scale so that they will match the L and W that are at the left and right sides of the pattern.
    When that is done, then,
    2L = 3W
    So,
    L = 1.5W

    Thus, the pattern is (W +W +W) high by (W +L) wide.
    That is, the pattern is 3W high by 2.5W wide.

    So if the area to be covered is 12L long by 10L wide, then, in terms of W, that is
    (12*1.5)W long by (10*1.5)W wide
    Or,
    18W long by 15W wide.

    If there is no preferred way to lay out the pattern, other than the way to minimize cuttting, then we lay them out such that the width of the pattern is along the width of the area to be covered.
    Becauce, along the width of the area, 15W / 2.5W = 6 patterns
    And along the length of the area, 18W / 3W = 6 patterns too.

    So the are 6*6 = 36 patterns all in all to cover the area exactly.

    In one pattern there are 5 rectangles that are L by W.
    Therefore, 36*5 = 180 rectangles are needed. ----------answer.
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  3. #3
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    Thank you so much. You are very helpful!
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