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 ...
- Solid Mensuration - The area of a regular hexagon inscribed in a circle is equal...
- geometry - A square ABCD is inscribed in a circle. The circle is folded to form ...
- 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 ...
- math - 1. A wire of length x is bent into the shape of a square. Express the ...
- calculus - Find the dimensions of the rectangle with the largest area that is ...
- Calculus - Find the area of the largest rectangle that can be inscribed in a ...