The length of a rectangle is 7 ft less than three times the width, and the area of the rectangle is . Find the dimensions of the rectangle.

Question

The length of a rectangle is 7 ft less than three times the width, and the area of the rectangle is . Find the dimensions of the rectangle.

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Ngọc Hoa 6 months 2021-08-04T06:49:25+00:00 1 Answers 8 views 0

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    2021-08-04T06:50:57+00:00

    Answer:

    See explanation

    Step-by-step explanation:

    the length of a rectangle is 7 feet less than three times it’s width. if the area of the rectangle is 180 ft, find the dimensions of the rectangle.

    Width = x

    Length = 3x – 7

    Area of a rectangle = length × width

    180 = (3x – 7) * x

    180 = 3x² – 7x

    3x² – 7x – 180 = 0

    Using quadratic formula

    a = 3

    b = -7

    c = -180

    x = -b ± √b² – 4ac / 2a

    x = -(-7) ± √(-7)² – 4(3)(-180) / 2(3)

    x = 7 ± √49 – (-2160) / 6

    = 7 ± √49 + 2160 / 6

    x = 7 ± √2209/6

    = 7 ± 47 / 6

    = (7 + 47)/6 or ( 7 – 47)/6

    = 54/6 or -40/6

    x = 9 or -6.67

    x cannot be negative

    Therefore,

    x = 9 ft

    Width = x = 9 ft

    Length = 3x – 7

    =3(9) – 7

    = 27 – 7

    = 20 ft

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