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Math Help - Quadratics

  1. #1
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    Quadratics

    The question:

    In a right angled triangle the second to longest side is 5cm longer than the shortest and the hypotenuse is 3 times longer than the shortest side. Find the exaact length of the hypotenuse.

    The answer is (15+30 root2)/7

    But I got this 5+root50 through the following working:
    Could you please tell me where I went wrong?
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  2. #2
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    The right hand side should be 9x^2
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  3. #3
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    umm why?
    Last edited by mr fantastic; June 6th 2009 at 08:29 PM. Reason: Restored original post so the the subsequent posts have a context.
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  4. #4
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    Because both the 3 and x have to be squared:

    \begin{aligned}<br />
x^2 + (x + 5)^2 &= (3x)^2 \\<br />
x^2 + x^2 + 10x + 25 &= 9x^2 \\<br />
2x^2 + 10x + 25 &= 9x^2 \\<br />
0 &= 7x^2 - 10x - 25<br />
\end{aligned}

    Then solve using the quadratic formula.


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  5. #5
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    Your working should be something like this

    a + b = c
    (x)+ (5+x) = (3x)
    x + 25 + 10x + x = 9x
    2x +10x + 25 =9x
    7x- 10x -25 = 0

    Use quad formula from here to get answer.
    Last edited by Joel; June 6th 2009 at 08:24 PM. Reason: addition corection
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  6. #6
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    Oh could you tell me how I messed up in the quadratic formula then?



    ^ My answer is (5+/- 10root2)/7 rather than ( 5+/- 30root2 )/7
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  7. #7
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    7x-10x-25=0

    Using quad

    = -(-10) + root of (-10) - 4 (7) (-25)
    Divided by 2(7)

    =10 + root of 100 + 700
    divided by 14


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  8. #8
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    Firstly:
    why is it 100-700 --> -4 * 7 *-25 should be positive since there are two negatives multiplying against one another

    Secondly:
    if it is 100-700 then it will be a NEGATIVE number which cannot square root and therefore the answer will be "no real solutions" which is even more incorrect
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  9. #9
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    Um how did you get that?
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  10. #10
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    7x^2 - 10x - 25 = 0

    \begin{aligned}<br />
x &= \frac{10 \pm \sqrt{(-10)^2 - 4(7)(-25)}}{2(7)} \\<br />
&= \frac{10 \pm \sqrt{100 + 700}}{14} \\<br />
&= \frac{10 \pm \sqrt{800}}{14} \\<br />
&= \frac{10 \pm 20\sqrt{2}}{14} \\<br />
&= \frac{5 \pm 10\sqrt{2}}{7}<br />
\end{aligned}
    Hmm, I'm not getting the original answer. I'm getting what prettiestfriend got.


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