Answer
Largest Area that can be enclosed = 361250 m²
Step-by-step explanation
Let the length of the fencing along the river be L
Let the width of the fencing be W
A sketch of the problem will make it clearer
Perimeter = L + 2W
Perimeter is giving as the total length of the fencing to be 1700 m
L + 2W = 1700
L = 1700 - 2W
The area of the structure is given as
Area = LW
The area is what we want to maximize
Recall, L = 1700 - 2W
Area = LW = (1700 - 2W) × W = 1700W - 2W²
A = 1700W - 2W²
At maximum point, the derivative of any function is zero
Hence,
(dA/dW) = 1700 - 4W
At maximum point,
(dA/dW) = 0
1700 - 4W = 0
4W = 1700
Divide both sides by 4
(4W/4) = (1700/4)
W = 425 m
Recall, L = 1700 - 2W
L == 1700 - 2(425)
L = 1700 - 850
L = 850 m
Maximum Area
= (Length at maximum area) × (Width at maximum area)
= 850 × 425
= 361250 m²
Hope this Helps!!!