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.
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