Question

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.

Answer 1

Width  = 55 yards

Length   =  165 yards

Maximized area   =  9075 sq yd

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 = $(\frac{-b}{2a} ) = \frac{-330}{2\times (-3)} = 55$

So, W = 55 yards

Now, L = (390 - 3 (55) ) =  165 yards

Now, maximized area  = L x W

= 55 x 165  = 9075 sq yds