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11 June, 09:58

The length of a rectangle is 2 units more than the width. The area of the rectangle is 63 units. What is the length, in units, of the rectangle?

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  1. 11 June, 11:21
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    Length = 9units

    Width = 7units

    Step-by-step explanation:

    It is said that the length is 2units more than the width

    Assume that the width is x, then the length will be 2 + x

    ie

    Width = x

    Length = 2 + x

    Area of the rectangle = 63units

    Area of rectangle = l * b

    l - length of the rectangle

    b - width of the rectangle

    A = l * b

    63 = (2 + x) * x

    63 = (2 + x) x

    63 = 2x + x^2

    Let's rearrange it

    x^2 + 2x - 63 = 0

    Let's find the factor of 63

    A factor that can be multiplied to give - 63 and that can be added to give + 2

    Let's use - 7 and + 9

    x^2 - 7x + 9x - 63 = 0

    Separate with brackets

    (x^2 - 7x) + (9x - 63) = 0

    x (x - 7) + 9 (x - 7) = 0

    (x + 9) (x - 7) = 0

    (x + 9) = 0

    (x - 7) = 0

    x + 9 = 0

    x = - 9

    x - 7 = 0

    x = 7

    Note: the length of a rectangle can not be negative

    So therefore,

    x = 7

    Length = 2 + x

    = 2 + 7

    = 9units

    Width = x

    = 7units
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