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A rectangle has an area of 60 square inches and a perimeter of 38 inches. Find the length and width if the rectangle.

  • math -

    The dimensions for the area must be either
    10 * 6
    or
    12 * 5
    or
    15 * 4

    Which of those sets of dimensions will give you a perimeter of 38 inches?


    Which

  • math -

    L * W = 60 sq in
    W = 60/L
    2L + 2W = 36 IN
    Substitute 60/l for w:
    2L + 2*60/L = 36
    2L + 120/L = 36
    Multiply both sides by L:
    2L^2 + 120 = 36L
    L^2 + 60 = 18L
    L^2 - 18L + 60 = 0
    Use Quadratic formula to find l:
    L = 9 +- sqrt(21) = 9 +- 4.58
    L = 13.58, and 4.42.
    13.58 * W = 60, W = 4.42 IN
    4.42 * W = 60, W = 13.57 in

    2 Solutions: L * W =13.58 * 4.42 and
    L * W = 4.42 * 13.58.

  • math -

    OOPS!! I used 36 for the perimeter.
    It should be 38. Sue made the same error.

    L * W = 60 IN^2, W = 60/L
    2L + 2W = 38 IN
    2L + 2 *60/L = 38
    2L + 120/L = 38
    2L^2 + 120 = 38L
    L^2 + 60 = 19L
    L^2 - 19L + 60 = 0
    (L - 4) (L - 15) = 0
    L = 4, and 15.

    2 solutions: L = 4, W = 15.
    L = 15 , W = 4.

  • math -

    NO, SUE DID NOT MAKE THE ERROR THAT
    I MADE!

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