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8 June, 03:00

The length of one side of a square is (x + 2 1/4). If the perimeter is 14 units, what is the area?

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  1. 8 June, 06:35
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    The perimeter is the total of adding all of the side lengths together.

    A square has 4 equal side lengths.

    So the perimeter of a square is:

    P = s + s + s + s or P = 4s

    [P = perimeter s = side lengths of the square]

    Since you know the side length of the square is (x + 2 1/4), you can replace s with (x + 2 1/4)

    P = 4s

    P = 4 (x + 2 1/4) Multiply 4 into (x + 2 1/4)

    P = 4x + 8 4/4

    P = 4x + 9

    Since you know the perimeter, you can plug it in. (you could have also plugged it in in the beginning)

    P = 4x + 9

    14 = 4x + 9 Subtract 9 on both sides

    5 = 4x Divide 4 on both sides

    5/4 = x

    Now that you know x, find the side length of the square.

    (x + 2 1/4)

    (5/4 + 2 1/4)

    2 6/4 = 3 2/4 = 3 1/2 units or 3.5 units

    To find the area of a square, you multiply 2 of the sides together:

    A = s · s

    A = 3.5 · 3.5

    A = 12.25 units²
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