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Math Help - Rhombus Pythagorean!

  1. #1
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    Rhombus Pythagorean!

    Each side of a rhombus measures 12 in. If one diagonal is18 in. long, how long is the other diagonal?

    So what I did is. Constructed a rhombus. Made each side 12 in and made a diagonal of 18. I make another diagonal and so I get 4 right angles

    I choose 1. I have 12 as c^2 and 9 as a^2 now. I need to find B^2

    9^2 = 81 + b^= 144

    b = 63

    correct answer is --- > 6√7


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  2. #2
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    Re: Rhombus Pythagorean!

    I'm not sure what the question is, your reasoning is correct. Just remember that the b you found is only half the length of the diagonal.
    b = sqrt(63) = sqrt(9 * 7) = 3*sqrt(7)
    2*b = 6 sqrt(7)
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  3. #3
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    Re: Rhombus Pythagorean!

    Just to find the length of the other diagonal.
    Multiplying 3*sqrt(7) by 2 equals the correct answer. But Whats the reasoning for multiplying 3*sqrt(7) by 2?
    The correct answer is 6sqrt(7) but I didn't seem to get it.
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  4. #4
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    Re: Rhombus Pythagorean!

    Quote Originally Posted by Cake View Post
    Just to find the length of the other diagonal.
    Multiplying 3*sqrt(7) by 2 equals the correct answer. But Whats the reasoning for multiplying 3*sqrt(7) by 2?
    The correct answer is 6sqrt(7) but I didn't seem to get it.
    The diagonals of a rhombus bisect one another at right angles.
    Thus you found only one-half of its length. That is why we multiply by two.
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