Question 175757
x = width, y = length, A = area

2x + y = 60
y = 60 - 2x
 
A = xy
 
Substitute y = 60 - 2x.
A = xy
= x(60 - 2x)
= -2x^2 + 60x
 
Complete the square.
-2x^2 + 60x = -2(x^2 - 30x)
= -2(x^2 - 30x + 225) + 450
= -2(x - 15)^2 + 450
 
The maximum is 450 at x = 15.
 
The dimensions of the fencing should be 15m by 30m.