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# greatest area of a rectangle inscribed in a circle

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Manager
Joined: 05 Oct 2005
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greatest area of a rectangle inscribed in a circle [#permalink]  02 Jun 2006, 09:51
hello
does anyone have the mathematically correct way to compute the greatest area of a rectangle inscribed in a circle given its diameter D

thanks
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Director
Joined: 04 Jan 2006
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this is interesting.. i would like to be in the loop if someone does get the answer!
VP
Joined: 29 Dec 2005
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Re: greatest area of a rectangle inscribed in a circle [#permalink]  02 Jun 2006, 20:05
2
KUDOS
mand-y wrote:
hello
does anyone have the mathematically correct way to compute the greatest area of a rectangle inscribed in a circle given its diameter D
thanks

i like the question.

square is the greatest ractangal that can be inscribed in the circle with diameter D.
S = side of the square
S^2+S^2 = D^2
S = D/sqrt(2)

A (area of the square) = D^2/2

if D = 10, A = 50.
VP
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Prof is right. I don't think we need to know how to prove this, but it requires differentiation..

Area = l*w

d^2 = l^2+w^2
=>w = SQRT(d^2-l^2)

Hence A = l*(d^2-l^2)^1/2

To find the maxima of this fn, we ned to differentiate this eqn and set
dA/dl = 0
=> 2*l^2 = d^2
=> l = d/SQRT(2) & w = d/SQRT(2)
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