A carpenter is building a rectangular room with a fixed peri

A carpenter is building a rectangular room with a fixed perimeter of 240 ft. What dimensions would yeild the maximum area? what is the maximum area?

perimeter of the rectangulatr room=240ft
perimeter of a rectangle=2*(l+b)
so 240=2*(l+b)so
l+b=120
so if l=x
b=120-x
area=x*(120-x)
A=x(120-x)
for maximum A dA/dx=0
dA/dx=d/dx(120x-x^2)
0=120-2x
x=60ft
length=60ft
breadth=120-60=60ft answer