Let be the diameter, the center of the circle, the rectangle, with .

Let . Then the area is .

We have .

If the area is maximum, then the squared area is also maximum.

Let and

The maximum value of f is , where .

So, , for .

Then

Results 1 to 5 of 5

- Jun 15th 2008, 07:54 AM #1

- Joined
- Jun 2008
- Posts
- 12

- Jun 15th 2008, 08:18 AM #2

- Jun 15th 2008, 09:04 AM #3

- Jun 15th 2008, 09:10 AM #4

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 5

- Jun 15th 2008, 10:16 AM #5
Here is what I was doing until I realized I used the wrong radius.

Sorry if it seems redundant since RedDogs fine answer, but I worked it out earlier and do not want my attempt to go in vain.

Let x and y be the dimensions of the rectangle. Then area is**A=xy**

But

This means

Sub into A and we have:

Max area is then

Now, try the same problem with an inscribed trapezoid