geometry
posted by lily on .
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

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.