Posted by Evie on Saturday, April 19, 2008 at 12:33am.
Show that the rectangle with the largest area that is inscribed within a circle of radius r is a square. Find the dimensions and the area of the inscribed square.
My respect goes to those who know how to tackle this one.

Calculus  Reiny, Saturday, April 19, 2008 at 7:56am
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

Calculus  Evie, Saturday, April 19, 2008 at 6:02pm
Thank you so much. I appreciate you taking the time to answer my question. = )
Answer This Question
Related Questions
 Geometry  Circle O is inscribed is square ABCD, and at the same time, is ...
 calculus  There is a shape first a regular triangle inscribed in a circle, and ...
 Solid Mensuration  The area of a regular hexagon inscribed in a circle is equal...
 math  if the area of the square inscribed in a semicircle is 2cm^2,find the ...
 geometry  A square ABCD is inscribed in a circle. The circle is folded to form ...
 Math  If area of a square inscribed in a semi circle is 2 square centimeter. ...
 Calculus  Hello, could someone please help me with this problem? I'm a little ...
 calculus  Find the dimensions of a rectangle with maximum area that can be ...
 calculus  A rectangle is to be inscribed under the arch of the curve y=4cos(.5x...
 Math  Find the shaded area in the following figure if the rectangle inscribed ...
More Related Questions