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Math Help - Rectangle's Dimensions

  1. #1
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    Rectangle's Dimensions

    A rectangle has a perimeter of 23cm. Its area is 33cm². Determine the dimensions of the rectangle.

    Can anyone help?
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    Quote Originally Posted by xcompulsion View Post
    A rectangle has a perimeter of 23cm. Its area is 33cm². Determine the dimensions of the rectangle.

    Can anyone help?
    Perimeter:

    2l + 2w = 23.


    Area:

    l\,w = 33.


    Solve these equations simultaneously.
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    Quote Originally Posted by Prove It View Post
    Perimeter:

    2l + 2w = 23.


    Area:

    l\,w = 33.


    Solve these equations simultaneously.
    Hi again, could you maybe help me start it off?
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    Quote Originally Posted by xcompulsion View Post
    Hi again, could you maybe help me start it off?
    Use one of the equations to isolate a variable, then substitute that into the other equation, for example

    lw = 33

    l = \frac{33}{w}

    Substitute:

    2l + 2w = 23

    2\left(\frac{33}{w}\right) + 2w = 23

    66 + 2w^2 = 23w

    Solve for w, then use either equation to find l given w.
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    Quote Originally Posted by undefined View Post
    Use one of the equations to isolate a variable, then substitute that into the other equation, for example

    lw = 33

    l = \frac{33}{w}

    Substitute:

    2l + 2w = 23

    2\left(\frac{33}{w}\right) + 2w = 23

    66 + 2w^2 = 23w

    Solve for w, then use either equation to find l given w.
    okay so after solving for w,

    66 + 2w^2 = 23w

    66 + 2w^2 - 23w = 0

    (w - 6)(w - 5.5) = 0

    so does w = 6, or 5.5?
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    This just means that there are two rectangles that could have these dimensions.

    Substitute both into the perimeter formula and solve for l.
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    Quote Originally Posted by Prove It View Post
    This just means that there are two rectangles that could have these dimensions.

    Substitute both into the perimeter formula and solve for l.
    Substitute both of them? I'm sorry, I don't really understand.
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    Quote Originally Posted by xcompulsion View Post
    Substitute both of them? I'm sorry, I don't really understand.
    If you take w = 6, you will get l = 5.5.

    If you take w = 5.5, you will get l = 6.

    You get the same rectangle either way :-)
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  9. #9
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    Quote Originally Posted by xcompulsion View Post
    Substitute both of them? I'm sorry, I don't really understand.
    Substitute one of them into the equation. Solve for l.

    Then pretend you hadn't done that, and substitute the second into the equation. Solve for l.
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  10. #10
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    Oh! Okay, I understand now.

    Thanks a lot.
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