Question

The owner of the Rancho Grande has 3,060 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose?

Answer 1

1170450 yd^2

Explanation:

The first thing is to calculate the necessary perimeter, which would be like this:

2 * a + b = 3060

if we solve for b, we are left with:

b = 3060-2 * a

Now for the area it would be:

A = a * b = a * (3060-2 * a )

A = 3060 * a -2 * a ^ 2

To maximize the area, we calculate the derivative with respect to "a":

dA / da = d [3060 * a -2 * a ^ 2

]/gives

dA / day = 3060 - 4 * a

If we equal 0:

0 = 3060 - 4 * a

4 * a = 3060

a = 3060/4

a = 765 and d

Therefore b:

b = 3060 - 2 * a = 3060 - 1530 = 1530

A = a * b

A = 765 * 1530

A = 1170450 and d ^ 2