sue has 100 ft of fencing she wants to put around a rectangular area next to her barn the barn will form one side of that area. Find the dimension that will enclose the maximum area. Find the maximum area
+128460 Let x be the number of feet of fence on each side of the area perpendicular to the barn
So......the side parallel to the barn is (100 - 2x)
So....the area, A = x(100 - 2x)
A = -2x^2 + 100x
This will be a parabola turning downward
The x coordinate that maximizes the area is given by the x coordinate of the vertex =
-100 / [ 2 * -2] = -100 / -4 = 25 ft = x
So....the dimensions are (25) (100 - 25) = 25 ft x 75 ft
And the max area is 25 * 75 = 1875 ft^2
