A rancher wants to use 400 feet of fencing to enclose a rectangular area of 6400 square feet. what dimensions should the rectangle have?

Lets l to be lenght, w width, p perimeter and a area:

a=lw

6400 ft²=lw

2 (l+w) = p

2 (l+w) = 400 ft

l+w = 200 ft

l=200ft-w

substitute it instead of l to lw=6400ft²

(200-w) w=6400

200w-w²=6400

w²-200w+6400=0

(w-160) (w-40) = 0

w = 160ft

w = 40ft

l=200-w

l=200-160 = 40ft

l = 200-40 = 160ft