Carl want to construct three rectangular dog-training arenas side-by-side using a total of 450 feet of fencing. What should the overall length and width be in order to maximize the area of the three combined areas.

2(3l+b)=450.

3l+b=225.

area A=3lb.

for area to be maximum 3l=b.

2*2b=450.

b=112.5 ft.

l=b/3 =112.5/3

=37.5 ft.

overall length =3l=3*37.5 =112.5 ft.

width b=112.5. ft.