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Math Help - Maximum area of rectangle with given perimeter.

  1. #1
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    Maximum area of rectangle with given perimeter.

    Find the maximum area of a rectangular piece of ground that can be enclosed by 100 m of fencing

    any help would be great!
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  2. #2
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    Quote Originally Posted by scubasteve94 View Post
    Find the maximum area of a rectangular piece of ground that can be enclosed by 100 m of fencing

    any help would be great!
    A = xy.

    100 = 2x + 2y => y = 50 - x.

    Therefore A = x(50 - x). This is a parabola. Find the A-coordinate of its maximum turning point.
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  3. #3
    Junior Member BobBali's Avatar
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    Area = -X^2 + 50x

    Solve for vertex using line of symmetry equation x = - b/2a

    x = -50/-2 , x = 25
    Hence, find y by substituting back into y = -2x+50
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