geometry

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given constant perimeter (people),Irene made a rectangle with an area (tables) of 196 sq. units. she finds that this is the largest area (greatest number of tables) possible for the given perimeter. Irene drew a rectangle with an area of 196 sq. units. she finds that this i the largest area possible for any rectangle with the same perimeter. what are the dimensions of the rectangle and what is the perimeter of the retangle

  • geometry -

    Considering all possible rectangles with a given perimeter, the square encloses the greatest area.

    Proof:
    Consider a square of dimensions "x "by "x", the area of which is x^2.
    Adjust the dimensions by adding "a" to one side and subtracting "a" from the other side.
    This results in an area of (x + a)(x - a) = x^2 - a^2.
    Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.

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