What are the dimensions of a rectangle of a fixed perimeter P that result in the largest area?

NOTE: What exactly is a fixed perimeter?

Printable View

- Jan 24th 2007, 01:50 PMsymmetryRectangle Dimensions
What are the dimensions of a rectangle of a fixed perimeter P that result in the largest area?

NOTE: What exactly is a fixed perimeter? - Jan 24th 2007, 02:24 PMAfterShock
- Jan 24th 2007, 06:07 PMsymmetryok
Okay...but where did you get p/4?

- Jan 24th 2007, 07:03 PMAfterShock
Every side of a square is equal, and therefore the perimeter of a square is:

x + x + x + x, where x is the length of a side,

Or similarly, 4x = P, where P is the perimeter

P/4 = x, which is a side of the square

Thus, the dimensions that result in the largest area has to be P/4 by P/4. - Jan 25th 2007, 01:46 AMearboth
- Jan 25th 2007, 02:16 AMearboth
Hello,

to demonstrate what a fixed perimeter means I've attached a digram which shows rectangles which have all the perimeter 16 cm. As you may see the size of those rectangles differs a lot. You'll find the rectangle with the greatest size in the middle of the triangle. I've drawn this square with some thicker perimeter.

Hope this helps a little bit further.

EB - Jan 25th 2007, 04:19 PMsymmetryok
I thank you for the notes.

Earboth:

You have outdone yourself here. All your replies with diagrams are the best I've seen.