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Math Help - Geometry (Pythagoras)

  1. #1
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    Geometry (Pythagoras)

    If anyone can help me with this questions that would be great!!

    The hypotenuse of a right triangle is 3.00ft longer than one of the sides, which in turn is 5.00ft longer than the other side. How long are the sides and the hypotenuse?

    Thanks a lot!
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by stephie View Post
    If anyone can help me with this questions that would be great!!

    The hypotenuse of a right triangle is 3.00ft longer than one of the sides, which in turn is 5.00ft longer than the other side. How long are the sides and the hypotenuse?

    Thanks a lot!
    Let's call the smallest side "x"

    Therefore we have: x^2 + (x + 5)^2 = ( (x + 5) + 3)^2

    Or in other words: x^2 + (x + 5)^2 = (x + 8)^2

    Therefore: x^2 + x^2 + 10x + 25 = x^2 + 16x + 64

    Subtract both sides by x^2 to get: x^2 + 10x + 25 = 16x + 64

    Take 25 from both sides: x^2 + 10x = 16x + 39

    Put it all on one side: x^2 - 6x - 39 = 0

    Quadratic equation: x = [ -b +/- SQRT( b^2 - 4ac ) ] / ( 2a )

    Substitute: x = [ -(-6) +/- SQRT( [-6]^2 - 4[1][-39] ) ] / ( 2[1] )

    Which eventually becomes x ~ 9.92820323 and x ~ -3.92820323

    x can't be negative, so: x = 9.92820323 = 3 + 4[ SQRT(3) ]

    So one side is 3 + 4[ SQRT(3) ]

    The other is 8 + 4[ SQRT(3) ]

    And the hypotenuse is: 11 + 4[ SQRT(3) ]
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  3. #3
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    I came up with a different answer for this:

    Let x = the side that the hyp is 3 more than
    Let x-5 = the other side

    x^2 + (x - 5)^2 = (x + 3)^2

    resolves to:

    x^2 - 16x + 16

    = (16 +/- sqrt(16^2 - 4(16))) / 2

    = 8 +/- 4sqrt(3)

    x = approx. 14.93 or x = approx 1.07

    if x = 14.93 then the sides are 14.93 and 9.93 and the hyp is 17.93

    14.93^2 + 9.93^2 = 17.93^2 = approx 321.5 checks

    if x = 1.07 then the sides are 1.07 and -3.93 ....impossible
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  4. #4
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Quick View Post
    The other is 8 + 4[ SQRT(3) ]
    Quote Originally Posted by spiritualfields View Post
    = 8 +/- 4sqrt(3)
    We came up with the same answer
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  5. #5
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    thanks a lot everyone. You have been a great help!
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  6. #6
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    We came up with the same answer
    Sure did. Not sure how I missed that. It was late and I was tired, I guess.
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