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Math Help - Find the area given the perimeter

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    Find the area given the perimeter

    The length is 35 yards and the perimeter is 120, what is the area?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Erynn S View Post
    The length is 35 yards and the perimeter is 120, what is the area?
    ...what's the figure? a rectangle?

    if so, let the width be x

    then the perimeter is 2x + 2(35) = 120

    and the area is given by A = 35x

    now, can you find A with the given information?
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  3. #3
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    Quote Originally Posted by Erynn S View Post
    The length is 35 yards and the perimeter is 120, what is the area?
    It's simpler than it seems .

    You have should know two equations by this point in math: Area and Parameter.

    In this problem you're going to combine them. To do this let's first list our two equations.

    Area = length * width
    Parameter = (2 * length) + (2 * width)

    Do you see anything these two equations have in common? They both share the same two variables: length and width.

    The next thing you do is list what you have. Here it is:

    Parameter = 120 yards
    length = 35 yards

    You have information for two variables here. You have length and the parameter. So what should you do with them? Well, the question asks you to find the area. But to find the area you need to know the length as well as the width. But you only have the length.

    To find the width you'll have to use the Parameter equation. You already know two variables that fit into it, Parameter and length. So let's plug them in:

    120 yards = (2 * 35 yards) + (2 * width)

    That should look familiar. It's a simple one-variable equation that you've seen a million times. That's the same as saying 120 = 70 + 2x. The "x" in this case is the width (which we need in order to solve for area). So we solve the equation for width!

    First we simplify it:
    120 yards = 70 yards + 2 * width
    Next, we subtract 70 from bothsides:
    50 yards = 2 * width
    Finally, we divide both sides by two:
    25 yards = width

    Now we have our width! That's all we need to solve for area. Now we just plug everything into the Area equation:

    Area = 35 yards * 25 yards
    We solve for Area and we get:
    Area = 875 yards * yards
    or:
    Area = 875 yards^2 (yards squared)

    There you go! Wasn't too hard, was it?
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