Answer:
y = 70 yd
A(max) = 9800 yd²
Step-by-step explanation:
Let call " y " sides of the rectangular area running perpendicular to the river, then:
Perimeter of the area (without one side is )
P = x + 2*y and we have 280 yards of fencing material
280 = x + 2*y ⇒ y = ( 280 - x ) / 2
And rectangular area is:
A = x*y
Area as a function of x is:
A(x) = x * ( 280 - x ) / 2
A(x) = 280*x /2 - x²/2
Taking derivatives on both sides of the equation we get:
A´(x) = 140 - x = 0
140 - x = 0
x = 140 yd
And y
y = ( 280 - x ) / 2
y = 140 /2
y = 70 yd
And
A( max ) = 140*70
A(max) = 9800 yd²