The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length, in units, of the rectangle.

Question

The width of a rectangle is the length minus 6 units. The area of the rectangle is 27 units. What is the length, in units, of the rectangle.

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Everleigh 1 week 2021-11-20T20:32:24+00:00 1 Answer 0 views 0

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    2021-11-20T20:33:54+00:00

    Answer:

    Length=9\,\,units

    Step-by-step explanation:

    Let, the length of the rectangle be ‘L’

    Width of the rectangle be ‘W’

    Width=Length-6\\\\W=L-6

    Area of the rectangle=27\,\,units

    Area of a rectangle= Length\times Width

    27=Length\times Width

    27=L\times (L-6)

    L^2-6L=27\\\\L^2-6L-27=0

    L^2+3L-9L-27=0\\\\ L(L+3)-9(L+3)=0\\\\(L+3)(L-9)=0\\\\

    Equating to zero:

    L+3=0\\L=-3

    OR, Similarly:

    L=9 units

    The length of the rectangle cannot be negative,

    therefore,

      Length=9\,\,units

    W=L-6\\\\W=9-6\\\\W=3\,\,units

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