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10 December, 09:46

Kelly is gluing rectangular cards in her scrapbook. Each card has an area of 24 square inches and the length is 2 inches more than the width. If x represents the width of each card, select all of the equations that could be used to find the length and width of her cards.

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  1. 10 December, 10:03
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    The equation would be (w+2) (w) = 24, the width would be 4 and the length would be 6.

    We find the area of a rectangle by multiplying its length and width:

    A = lw

    The length is 2 more than the width, or l = w+2:

    A = (w+2) (w)

    24 = (w+2) (w)

    Multiplying this through, we have:

    24 = w² + 2w

    We want the equation set equal to 0 to solve it, so subtract 24 from both sides:

    24 - 24 = w² + 2w - 24

    0 = w² + 2w - 24

    This is easily factorable, as 6 (-4) = - 24 and 6 + - 4 = - 2:

    0 = (w+6) (w-4)

    Using the zero product property, we know either w+6=0 or w-4 = 0, so w=-6 or w=4. A negative width makes no sense, so w = 4. This means l = w+2 = 4+2 = 6.
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