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Math Help - pythagoras theorem

  1. #1
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    pythagoras theorem

    a square and a rectangle have the same length diagonal. Find x
    square = 2 unknows sides
    and the rectangle = 4 by 7 cm
    Last edited by Math Help; August 22nd 2005 at 09:01 PM.
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  2. #2
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    i dont know how to post the diagram... to show all the question. if someone can tell me how to post it, i will.
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  3. #3
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    the length of the diagonal of any rectangle is:

    \sqrt{(side A)^{2} + (sibe B)^{2}}

    in this case sideA = 4 and sideB = 7.

    Can you take it from there?

    Hint: Once you know the diagonal you can work backwords to get the length of the side of the square.
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  4. #4
    hpe
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    Quote Originally Posted by [confused]
    a square and a rectangle have the same lenght diagonal. Find x
    square = 2 unknows sides
    and the rectangle = 4 by 7 cm
    Let x be the unknown side of the square, and let d be the length of the diagonal.

    Then by the Theorem of Pythagoras, applied to the square,  x^2 + x^2 = d^2 or  2 x^2 = d^2 , and by applying the theorem to the rectangle,  4^2 + 7^2 = d^2 . You should draw two pictures and label them to convince yourself, one for the square and one for the rectangle. Then explain the pictures to a friend.

    Equate the two terms, thus  2 x^2 = 4^2 + 7^2 = 65 . Therefore,  x^2 = \frac{65}{2} and x = \sqrt{\frac{65}{2}} .
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