Answer:
41,666.67m2
Step-by-step explanation:
Call W the Width and L the Length with 3 pieces.
The total length will be 2W + 3L
The Area is L*W
so,
A = L*W
2W+3L = 1000
Solve for L
3L = 1000-2W
L = (1000-2W)/3
subtitute for L into the first equation
A = L*W
A = W*(1000-2W)/3
A = (1000W - 2W^2)/3
Now, to find the max, set the 1st derivative = 0. I don't know if you know what that means, but...
dA/dW = 1000/3 - 4W/3 = 0
1000 - 4W = 0
W = 250 meters
Solve for L
2W+3L = 1000
500 + 3L = 1000
3L = 500
L = 166.67 m
Area = 250*500/3 = 41,666.67m2.
