1.

A three-sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. The enclosed area is to equal 1800 ft2. Find the minimum perimeter and the dimensions of the corresponding enclosure.

1 answer

If side x is parallel to the river,
xy=1800

The perimeter is

p = 2(x+y) = 2(x + 1800/x)
p is a max when 1 - 1800/x^2 = 0, or x = 30√2

So, the field is 30√2 by 30√2

As usual, maximum area (or minimum perimeter) is achieved by a square.