Math, Gr 10

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A rectangular field is to be enclose by 800 meters of fencing and the fourth side with be along the side of a barn.
A) What dimensions will give the maximum area?
B) What is the maximum area?

  • Math, Gr 10 -

    let the single side by y
    let the two other sides be x each

    so 2x+y = 800
    y = 800-2x

    area = xy
    = x(800-2x)
    = -2x^2 + 800x

    Since you rated this grade 10 , I will assume you don't have Calculus, so let's complete the square

    area = -2(x^2 - 400x <>+40000-40000)
    = -2( (x-200)^2 - 40000)
    = -2(x-200)^2 + 80000

    the max area is 80,000 m^2 and is obtained when
    x = 200 m, which makes y = 800-2(200) = 400 m

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