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March 28, 2017

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7) A rectangular pen can be constructed using the side of a barn as one boundary and 5500 ft. of fence to make the other three sides. Find the length and width of the rectangle to make the largest area.
Hint: Draw a picture- and label the sides of the rectangle. And solve the problem.

  • College math - ,

    let each of the two equal sides be x
    let the single side by y
    then y+2x = 5500
    y = 5500 - 2x

    area = xy
    = x(5500-2x)
    = -2x^2 + 5500

    Since you labeled it "college" math, I will assume you know Calculus

    d(area)/dx = -4x + 5500
    = 0 for a max of area
    4x = 5500
    x = 1375
    y = 5500-2(1375) = 2750

    the pen is 1375 ft by 2750 ft, with the side of 2750 parallel to the barn.

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