Question

3.1 Q19

Mona has 440 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum​ area?

Answer 1

let one length be x and the other be y

x + x + y + y = 440
2x + 2y = 440

Divide by 2 through ...
x + y = 220
y = 220 - x

Area = xy
Area = x(220 -x) = 220x -
`x^(2)`

Given that that max length of x will be -b/2a
a = -1 b = 220
x =
`(-220)/(-2)` = 110

x = 110
y = 220 - 110 = 110

Therefore max area = 110 x 110 = 12100 square yards