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Math Help - Help! Octagon

  1. #1
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    Help! Octagon

    The longest diagonal of a rectangular octagon varies directly as the length of a side. if a regular octagon with sides 6mm has a diagonal of lenth 23mm, how long is the diagonal of an octagon with side of 15cm?

    Is there a formula for this? I dont know where to start. thanks!
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by sallyann View Post
    The longest diagonal of a rectangular octagon varies directly as the length of a side. if a regular octagon with sides 6mm has a diagonal of lenth 23mm, how long is the diagonal of an octagon with side of 15cm?

    Is there a formula for this? I dont know where to start. thanks!
    notice I highlighted "directly"

    this means that as the length of a side increases, the diagonal of the octagon increases at a constant amount as well.

    Think of a line: y=mx

    where y is the diagonal, and x is the side.

    thus: y/x=m

    now substitute known values: 23/6=m

    now that gives equation: y=(23/6)x

    now substitute 15 for side length: y=(23/6)(15)=57.5

    so the diagonal is 57.5
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  3. #3
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    Quote Originally Posted by Quick View Post
    notice I highlighted "directly"

    this means that as the length of a side increases, the diagonal of the octagon increases at a constant amount as well.

    Think of a line: y=mx

    where y is the diagonal, and x is the side.

    thus: y/x=m

    now substitute known values: 23/6=m

    now that gives equation: y=(23/6)x

    now substitute 15 for side length: y=(23/6)(15)=57.5

    so the diagonal is 57.5
    I am no engineer but one is in millemeters and the other in centimenters!
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  4. #4
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    I am no engineer but one is in millemeters and the other in centimenters!
    than the answer is 57.5cm
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Quick View Post
    than the answer is 57.5cm
    Pet peeve warning!!

    ALWAYS convert your units before doing a problem. It leads to fewer mistakes. This one turned out to be correct but don't bet on it in the future.

    Pet peeve over. (Whew!)

    -Dan
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