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math

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David currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 4 feet shorter than twice its width. He decides the perimeter should be 60 feet.
Determine the dimensions, in feet, of his new garden. What would be the equation? Would it be 2w-4=60?

  • math -

    Two equations
    L = 2 W - 4
    2 L + 2 W = 60
    so
    2 (2W-4) + 2 W = 60
    4 W - 8 + 2 W = 60
    6 W = 68
    W = 11 1/3 = 11 feet 4 inches
    L = 22 2/3 - 4 = 18 2/3 = 18 feet 4 inches

  • math -

    But then when I do the perimeter for the width and length I would get more than 60.

  • math -

    Oh never mind I see what I did to make it more than 60.

  • math -

    But wait. How did you get the dimensions for the length and width the way you did?

  • math -

    well, 68/6 is 11.3333333333
    and
    2(11.333 etc) - 4 is 18.66666666
    I will add some comments
    Two equations

    L = 2 W - 4 given

    2 L + 2 W = 60 perimeter of rectangle = 2W+2L
    so
    2 (2W-4) + 2 W = 60 Use (2W-4) for L

    4 W - 8 + 2 W = 60 multiply parentheses out

    6 W = 68 adding 8 to both sides and combining like terms

    W = 11 1/3 = 11 feet 4 inches dividing by 6

    L = 22 2/3 - 4 = 18 2/3 = 18 feet 4 inches by going back to L=2W-4

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