Let x be one side and l be the other side of the plot. Perimeter = 2(x + l) 200 = 2(x + l) l = 100 - x
Area of this rectangle: A = (x)(l) A = x(100 - x) A = 100x - x²
To find the maximum value of the area, we differentiate with respect to x and equate to 0 dA/dx = 100 - 2x 0 = 100 -2x x = 50 l = 100 - 50 = 50 This means the area will be maximized when the sides of the rectangle are equal; that is, when it is a square.