A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 390 yd of fencing is available, find the largest total area that can be enclosed.

Step-by-step explanation:

Here, the total length of fencing available  =  390 yd

Let L = length of the side parallel to river

W = width of other 3 sides.

So, total fencing L  +  3 W =  390 yd

or, L  = 390 - 3 W

Now, Area of the field  = L x W

= (390 - 3 w) (W)

or, A  =  -3 W² + 330 W

The maximum value of above function is  at W =

So, W = 55 yards

Now, L = (390 - 3 (55) ) =  165 yards

Now, maximized area  = L x W

= 55 x 165  = 9075 sq yds

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step-by-step explanation: