Posted by **lily** on Sunday, March 20, 2011 at 5:15pm.

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 -
**tchrwill**, Monday, March 21, 2011 at 9:40am
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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