Posted by Evie on Saturday, April 19, 2008 at 12:33am.
Let the base of the rectangle be x, let its height be y units.
the diagonal would be the diameter of the circle and it length is 2r.
so x^2 + y^2 = 4r^2
Area of rectangle = xy
= x√(4r^2 - x^2)
d(Area)/dx = ......
= (4r^2 - 2x^2)/√(4r^2 - x^2)
set this equal to zero for a maximum area and solve to get
x = r√2
put this back into x^2 + y^2 = 4r^2
to get y = r√2
so x=y, proving the rectange is a square
Thank you so much. I appreciate you taking the time to answer my question. = )
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