1. ## largest area

I need your help for this problem: Demonstate that in all
rectangles which have the same compass the qudrate has the biggest area. I am waiting your answer now. Thanks

2. Originally Posted by blertta
I need your help for this problem: Demonstate that in all
rectangles which have the same compass the qudrate has the biggest area. I am waiting your answer now. Thanks
Is this Calculus? Let me assume I can use Calculus.

I understand that you mean, "Demonstate that in all rectangles that have the same perimeters, the square has the biggest area."

Perimeter, P = 2(L +w) ---------(1)
Area, A = w*L ---------------(2)

From (1),
L +w = P/2
L = P/2 -w

So,
A = w(P/2 -w)
A = (P/2)w -w^2
Differentiate both sides with respect to w,
dA/dw = P/2 -2w
Set that to zero,
0 = P/2 -2w
2w = P/2
4w = P ----------***

Substitute that into (1),
P = 2(L +w)
4w = 2L +2w
4w -2w = 2L
2w = 2L
L = w ---------meaning, length = width, which is a square.

Therefore, the rectangle that is a square has the biggest area.