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Math Help - area of a rectangle

  1. #1
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    area of a rectangle

    suppose the expression x^2+7x+12/(x+2)^2 represents the area of a rectangle

    find the expression for the perimeter of the rectangle
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    Quote Originally Posted by william View Post
    suppose the expression x^2+7x+12/(x+2)^2 represents the area of a rectangle

    find the expression for the perimeter of the rectangle
    What does x represent? The length of a side ....?

    And is it A = x^2 + 7x + \frac{12}{(x+2)^2} or A = \frac{ x^2 + 7x + 12}{(x+2)^2} ?
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    Quote Originally Posted by mr fantastic View Post
    What does x represent? The length of a side ....?

    And is it A = x^2 + 7x + \frac{12}{(x+2)^2} or A = \frac{ x^2 + 7x + 12}{(x+2)^2} ?
    The question says suppose the expression represents the area of a rectangle, find the expression for the perimeter of the rectangle. And it is the second equation, where 7x and x^2 are included in the numerator.
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    Quote Originally Posted by william View Post
    The question says suppose the expression represents the area of a rectangle, find the expression for the perimeter of the rectangle. And it is the second equation, where 7x and x^2 are included in the numerator.
    A = xy => y = A/x and you're given A. Then:

    Perimeter = 2x + 2y.
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    Quote Originally Posted by mr fantastic View Post
    A = xy => y = A/x and you're given A. Then:

    Perimeter = 2x + 2y.
    I am not exactly sure of what you are suggesting. Can you be a little more specific?

    My ideas on the question: factor the top: (x+4)(x+3)/(x+2)(x+2)
    then split it into two expressions?
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    Quote Originally Posted by william View Post
    I am not exactly sure of what you are suggesting. Can you be a little more specific?

    My ideas on the question: factor the top: (x+4)(x+3)/(x+2)(x+2)
    then split it into two expressions?
    You're given an expression for A. Divide that expression by x to get the other side of the rectangle: y = A/x.

    Then perimeter = x + x + y + y = 2x + 2y and the problem is answered.
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    Quote Originally Posted by mr fantastic View Post
    You're given an expression for A. Divide that expression by x to get the other side of the rectangle: y = A/x.

    Then perimeter = x + x + y + y = 2x + 2y and the problem is answered.
    Unless it's something really really stupid like you're expected to say

    A = \frac{(x+3)(x+4)}{(x+2)(x+2)} = \left(\frac{x+3}{x+2}\right) \cdot \left(\frac{x+4}{x+2}\right)

    and then you're meant to take \frac{x+3}{x+2} as the length and \frac{x+4}{x+2} as the width.

    Which is why I asked what x was.

    In which case all I can say is and hope that whoever set the question accidently sets their pants on fire.
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    Quote Originally Posted by mr fantastic View Post
    Unless it's something really really stupid like you're expected to say

    A = \frac{(x+3)(x+4)}{(x+2)(x+2)} = \left(\frac{x+3}{x+2}\right) \cdot \left(\frac{x+4}{x+2}\right)

    and then you're meant to take \frac{x+3}{x+2} as the length and \frac{x+4}{x+2} as the width.

    Which is why I asked what x was.

    In which case all I can say is and hope that whoever set the question accidently sets their pants on fire.
    haha! this is what i was thinking, but did not think it was that simple, although now I think it is, thank you for your help!
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    Quote Originally Posted by mr fantastic View Post
    Unless it's something really really stupid like you're expected to say

    A = \frac{(x+3)(x+4)}{(x+2)(x+2)} = \left(\frac{x+3}{x+2}\right) \cdot \left(\frac{x+4}{x+2}\right)

    and then you're meant to take \frac{x+3}{x+2} as the length and \frac{x+4}{x+2} as the width.

    Which is why I asked what x was.

    In which case all I can say is and hope that whoever set the question accidently sets their pants on fire.
    Then I would simply multiply (x+3/x+2) and (x+4/x+2) by two and then add them together, correct? Final being 2x^2+14/x^2+4
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    Quote Originally Posted by william View Post
    Then I would simply multiply (x+3/x+2) and (x+4/x+2) by two and then add them together, correct? Final being 2x^2+14/x^2+4
    Yes. And the fool who wrote the question will probably want you to simplify the answer.

    But 2x^2+14/x^2+4 is not correct. I get \frac{4x+14}{x+2}.
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    Quote Originally Posted by mr fantastic View Post
    Yes. And the fool who wrote the question will probably want you to simplify the answer.

    But 2x^2+14/x^2+4 is not correct. I get \frac{4x+14}{x+2}.
    i multiplied the expression to get (x^2+6/x^2+4) + (x^2+8/x^2+4) add the numerators and the denominator stays the same? what did i do wrong?
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    Quote Originally Posted by william View Post
    i multiplied the expression to get (x^2+6/x^2+4) + (x^2+8/x^2+4) add the numerators and the denominator stays the same? what did i do wrong?
    P = 2 \left(\frac{x+3}{x+2}\right) + 2 \left(\frac{x+4}{x+2}\right) = \frac{2(x+3) + 2(x+4)}{x+2} = \, ....
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  13. #13
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    Quote Originally Posted by mr fantastic View Post
    P = 2 \left(\frac{x+3}{x+2}\right) + 2 \left(\frac{x+4}{x+2}\right) = \frac{2(x+3) + 2(x+4)}{x+2} = \, ....
    I really appreciate the help, you are very kind!
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