Question

A rancher has 4,200 feet of fencing available to enclose a rectangular area bordering a river. He wants to separate his cows and horses by dividing the enclosure into two equal areas. If no fencing is required along the​ river, find the length of the center partition that will yield the maximum area.

Answer 1

Answer:

The center portion's length will be "700 ft".

Step-by-step explanation:

Let the center will be "x".

Given that, Length = 4200 feet

Now, Length

⇒  $L=3x+y$

⇒  $4200=3x+y$

⇒  $y=4200-3x$

As we know,

Area,

⇒  $A=Length\times breadth=x\times y$

⇒      $=x(4200-3x)$

⇒      $=4200x-3x^2$

So that the length or center portion or the area will be greater or maximum when:

⇒  $x=-\frac{4200}{2\times (-3)}$

⇒     $=\frac{-4200}{-6}$

⇒     $=700 \ ft$