Answer:
Dimension is 20m x 10m
Step-by-step explanation:
The area of the rectangular is 200 ft².
Let;
x = length of the side parallel to the river
y = length of each of the other two sides
Then xy = 200, so y = 200/x
Minimize: L = length of the fence
L = x + 2y
Thus,
L = x + 400/x, where x > 0
dL/dx = 1 - 400/x² = (x² - 400)/x²
Let dL/dx =0
Thus, x² - 400 = 0
x = ± 20
Since x can't be negative, x must be 20.
When 0 < x < 20, dL/dx < 0. So, L is decreasing.
When x > 20, dL/dx > 0. So L is increasing.
Therefore, L has a relative and absolute minimum when x = 20 m
y = 200/x = 200/20 = 10 m
The fence is shortest if the side parallel to the river has length 20 m and the other 2 sides each have length 10 m.
