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Math Help - Finding Perimeter of a rectangle when not given any side length

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    Finding Perimeter of a rectangle when not given any side length

    The question in particular is that I am given a rectangle where the length is 2 m less then twice the width. The perimeter is 86 m and I need to find the side length.

    I am aware the the answer is that the length is 28 and the width is 15, but I need to show this algebraically. Help would be much obliged.
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    Quote Originally Posted by DPXJube View Post
    The question in particular is that I am given a rectangle where the length is 2 m less then twice the width. The perimeter is 86 m and I need to find the side length.

    I am aware the the answer is that the length is 28 and the width is 15, but I need to show this algebraically. Help would be much obliged.
    Let width be x and length be y. We set up a system of linear equations:

    2x + 2y = 86
    2x - 2 = y

    Solve the sytem.
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    Quote Originally Posted by undefined View Post
    2x - 2 = y
    Not to sure how you deprived this from 2x+2y=86
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    Quote Originally Posted by DPXJube View Post
    Not to sure how you deprived this from 2x+2y=86
    The second equation is not derived from the first. It is derived from the problem statement: "the length is 2 m less then twice the width."
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    Okay. So then how do I solve for x?
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    Quote Originally Posted by DPXJube View Post
    Okay. So then how do I solve for x?
    This is a question about solving a system of (linear) equations, and the techniques are: elimination (multiply equations by nonzero constants and add them) and substitution (solve for a variable and substitute into another equation).

    So example of elimination: subtract the second equation from the first to get

    2y+2 = 86-y

    y = 28

    Example of using substitution:

    2x + 2(2x - 2) = 86

    6x = 90

    x = 15
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