Robert has a rectangular garden that is currently 180ft^2 and has a perimeter of 54ft He wants to increase the size of his garden by 5 ft in both directions. What will be the area of his expanded garden?


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  1. let the width be x
    let the length be y

    so we know 2x + 2y = 54
    x + y = 27
    and y = 27-x

    new width = x+5
    new length = y+5 = 27-x + 5 = 32-x

    Isn't area = length x width ?
    old garden:
    x(27-x) = 180
    -x^2 + 27x - 180 = 0
    x^2 - 27x + 180 = 0
    (x-15)(x-12) = 0
    x = 15 or x = 12
    then y = 12 or y = 15 (symmetric solution)

    so the garden was 15 by 12

    take it from there

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