Which is the optimal rectangular area obtainable with fencing material of length L =10 ?
These kind of optimization problems appear with equations of 2nd degree at age 15-18,
but this visual version can in my opinion also be examined at 11-14.
The calculus-analysis would look like this.
1) Let area be and circumference be and
has maximum value for .
2) Also examine the case where the wall is used .
has maximum value for
3) The circle has a greater area to circumference ratio than the rectangle ( or square ) :
ratio k = 0,07957747 > 0,0675 =
PS. Merci, thanks and credit to V. Launay for earlier development on Geogebra 3.0.
http://www.geogebra.org/en/upload/files/vlaunay/activite1.html
Differential calculus assuming that the derivative = 0 at maximum point yields
