A rancher has 2600 feet of fence to enclose a rectangular region that lies along a straight river.

Question

A rancher has 2600 feet of fence to enclose a rectangular region that lies along a straight river. If no fence is used along the river (see the figure), find the dimensions needed to enclose 5 acres of land. Recall that 1 acre = 43,560 ft².

(A,B)= Smaller value and (A,B)=Larger Value

Answer 1

Let x = length of fence on the side parallel to the river and let y = length of each of the other two sides.

Then, x + 2y = 2600. So, y = 1300 - 0.5x

Area = xy = x(1300 - 0.5x) = 217,800

0.5x² - 1300x + 217800 = 0

x = [1300 ± √ 1254400] = 2420 or -1120

Since x can't be negative, x = 2420 ft and y = 90 ft

Answer 2

1 acre=43,560.17sq/ft

* 5

xy=21780sq/ft

2x+y=2600

The best I can do is 21780^.5=466.69*3=1400ft.