A wire of length 8 meters is cut into two pieces. One piece is bent into a square, and the other is bent into a rectangle whose length is twice its breadth. Find the dimensions that maximize the combi

Step 1: Define variables and set up equations for perimeters and areas.
Let the side of the square be $s$.
Let the breadth of the rectangle be $b$ and its length be $l$.
From the problem statement:

• The total length of the wire is 8 meters.
• One piece forms a square with side $s$. Its perimeter is $P_s = 4s$. Its area is $A_s = s^2$.
• The other piece forms a rectangle whose length is twice its breadth, so $l = 2b$. Its perimeter is $P_r = 2(l+b) = 2(2b+b