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A lot which is 3 feet times as long as it is wide is enclosed by a walk 10 feet wide. The area of the lot is 1200 square feet more than that of the walk. Find the dimensions of the lot.

PLZ help and give a check if possible!

  • Mathematics -

    If the lot's width is w,

    w*3w = (w+2*10)(3w+2*10) - w*3w + 1200
    w = 40

    so, the lot is 40x120

    the total area is 60x140 = 8400
    the lot's area is 40x120 = 4800
    so, the walk's area is 3600
    and the lot's area is 1200 more than that

  • Mathematics -

    How would you solve the equation? Because i need to show full work

  • Mathematics -

    (w+2*10)(3w+2*10) = (w+20)(3w+20) so you just solve

    3w^2 = (w+20)(3w+20) - 3w^2 + 1200
    3w^2 = 3w^2+80w+400 - 3w^2 + 1200
    3w^2 - 80w - 1600 = 0
    (3w+40)(w-40) = 0
    w = 40 or -40/3

    If you can't do that, you have some serious reviewing to do.

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