Question

you have 140 yards of fencing to enclose a rectangular region. find maximum area of rectangle

Answer 1

let P = 140 yards = 2L + 2W, the perimeter P of the rectangle, L is the length, and W is the width of the rectangular region...
the area A = LW...

Answer 2

140 = 2(L + W)
70 = L + W
W = 70 - L eqn(1)

Answer 3

substitute W in area formula...
A = LW = L(70 - L) = 70L - L^2
applying completing the square...
L^2 - 70L + 1225 = -A + 1225
(L - 35)^2 = -A + 1225

Therefore the length L = 35 yards, the area A = 1225 sq. yards, then the width W = 70 - 35 = 35 yards... therefore the rectangular region is a SQUARE...