The owner of the Rancho Bar X wishes to use 2400 yards of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it into two parts by means of a piece of fencing perpendicular to the riverbank. No fencing is required along the river. What is the largest area that can be enclosed and what are its dimensions

Step-by-step explanation:

Let length be x and breadth be y.

Along the river no fencing is required so total boundary line of the rectangular land = x + y + y = x + 2y

add divider to it so total length

= x + 2y + y = x + 3y

x + 3y = 2400

area A = xy

y (2400 - 3y) = A

2400y - 3y² = A

For maximum area dA / dy = 0

2400 - 6y = 0

y = 400 yards.

x = 1200 yards

largest area = xy

= 48000 sq yards.