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Math Help - Deriving Quadratic Equations

  1. #1
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    Deriving Quadratic Equations

    please could you help me with this question.

    The perimeter of a rectangle is 34cm. given that the diagonal is of length 13cm, and that the width is x cm, derive the equation x^2 - 17x + 60 = 0.

    Hence find the dimensions of the rectangle.

    please help me, solve this problem.

    Maybe its me being thick.
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  2. #2
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    The perimeter is 2x+2y=34--->x+y=17

    Area: x^{2}+y^{2}=169

    Solve the first one for y and sub into the area:

    x^{2}+(17-x)^{2}-169=0

    Now, expand and solve the resulting quadratic.
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  3. #3
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    Thanks galactus

    But i don't under stand what u have done.

    The answer is 5cm x 12cm.

    Do you mean solve the equations as simultaneous equations.

    don't understand what you have done.

    Quote Originally Posted by galactus View Post
    The perimeter is 2x+2y=34--->x+y=17

    Area: x^{2}+y^{2}=169

    Solve the first one for y and sub into the area:

    x^{2}+(17-x)^{2}-169=0

    Now, expand and solve the resulting quadratic.

    don't understand what you have done.

    where did u get the formulas.

    are of rect = l x h

    perimenter = 2l + 2 H

    solve it, so i can see how u got the answer


    where did u get the 169 from
    Last edited by mr fantastic; December 26th 2008 at 07:42 PM. Reason: Merged three consecutive posts and removed large red font
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  4. #4
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    13^{2}=169.

    I just solved one equation for a variable and subbed into the other. That is all you have to do.

    Solve x+y=17 for y and sub into the diagonal:

    The diagonal is 13. So, by Pythagoras, we have x^{2}+y^{2}=13^{2}

    We have two equations with two unknowns, solve away. I pretty much showed all the steps in the first post.
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  5. #5
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    Thank you

    Quote Originally Posted by galactus View Post
    13^{2}=169.

    I just solved one equation for a variable and subbed into the other. That is all you have to do.

    Solve x+y=17 for y and sub into the diagonal:

    The diagonal is 13. So, by Pythagoras, we have x^{2}+y^{2}=13^{2}

    We have two equations with two unknowns, solve away. I pretty much showed all the steps in the first post.
    Thank you

    Understand what u have done,

    cheers
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