david has 800 feet of fencing to enclose a rectangular field

david has 800 feet of fencing to enclose a rectangular field. what is the largest area that can be enclosed?

Solution

Leght of fencing = perimeter

let length be l and width of fiels be w

Perimeter = 2l +2w = 800

l +w =400

Area,A = l*w

= l( 400- l) = -l^2 +400l

Maxmimum area would occur at the vertex of the quadratice equation i.e. l = -b/2a = -(400/2*(-1))

= 200 ft

b = 400-200 = 200ft

Maximum Area = l*w = 200*200 = 40000 sqft