Question

Marquise has 200200200 meters of fencing to build a rectangular garden.

Answer 1

Hence the maximum possible area is 2500 square meteres

Given the area of the rectangular garden expressed as;

$A(x)=-x^2+100x$

The maximum area occurs when dA(x)/dx = 0

$\frac{dA(x)}{dx} = -2x + 100\\0= -2x + 100\\ 2x = 100\\x = \frac{100}{2}\\x = 50$

Next is to get the maximum area possible. Substitute x = 50 into the original function as shown;

$A(50)= -50^2 + 100(50)\\A(50) = -2500+5000\\A(50) = 2500$

Hence the maximum possible area is 2500 square meters