algebra

A rectangle has a length that is 5 feet more than its width. The area of this rectangle is 84 square feet. What is the width and length of this rectangle?

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  1. L = Length

    W = Width

    A = Area

    L = W + 5

    A = W * L

    84 = W * ( W + 5 )

    84 = W ^ 2 + 5 W

    W ^ 2 + 5 W = 84 Add 25 / 4 to both sides

    W ^ 2 + 5 W + 25 / 4 = 84 + 25 / 4

    W ^ 2 + 5 W + 25 / 4 = 336 / 4 + 25 / 4

    W ^ 2 + 5 W + 25 / 4 = 361 / 4

    ( W + 5 / 2 ) ^ 2 = 361 / 4

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    Becouse:

    ( W + 5 / 2 ) ^ 2 =

    W ^ 2 + 2 * W * 5 / 2 + ( 5 / 2 ) ^ 2 =

    W ^ 2 + 5 W + 5 / 4

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    ( W + 5 / 2 ) ^ 2 = 361 / 4

    W + 5 / 2 = + OR - sqrt ( 361 / 4 )

    W + 5 / 2 = + OR - 19 / 2

    1 case :

    W + 5 / 2 = 19 / 2 Substract 5 / 2 to both sides

    W + 5 / 2 - 5 / 2 = 19 / 2 - 5 / 2

    W = 14 / 2 = 7 ft

    2 case :

    W + 5 / 2 = - 19 / 2 Substract 5 / 2 to both sides

    W + 5 / 2 - 5 / 2 = - 19 / 2 - 5 / 2

    W = - 24 / 2 = - 12 ft

    Width can't be negative, so:

    W = 7 ft

    L = W + 5 = 12 ft

    A = W * L = 7 * 12 = 84 ft ^ 2

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