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CCNYHelp

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A little Calculus 1 help...

I have a question,
"Find the dimensions of the largest rectangle to be inscribed in a circle of radius R"

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: A little Calculus 1 help...

The longest rectangle is about .99999999999999 times 2 times R for the length and height of .00001 or so.
The largest area is a square though, well I am just guessing it is a square.

Last edited by John E. Franklin (2007-12-08 03:59:40)

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igloo myrtilles fourmis

ccnyhelp

Guest

Re: A little Calculus 1 help...

how did you do that?

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: A little Calculus 1 help...

Assume the rectangle is a square. If it werent, then it would have less than the maximum possible area.
If you drew a line from one corner of the square to the other, you'd see it passes through the center of the circle. This means that the diagonal of the square is the diameter of the circle.
This diagonal also makes a triangle with two sides of the square, so we can use the pythagorean theorem to work out the sides of the square. Because the sides are the same, your equation looks like this:

d² = s² + s²
d = 2r, so:
(2r)² = s² + s²
(2r)² = 2s²
4r² = 2s²
2r² = s²
√(2r²) = s
√2* √r² = s
r*√2 = s

So the side of the square is the square root of 2 (approx 1.414) times the radius of the circle.

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.