a guy is creating a rectangular animal pen. he has 400 ft of fencing to use for this pen. what r the dimensions of the largest area of rectangle that can be enclosed by the fencing?
2007-04-10 14:21:20 · 5 answers · asked by singervv01 1 in Science & Mathematics ➔ Mathematics
A square is a special rectangle. It would yield the largest area. Therefore, the dimensions should be 100x100 ft. Just divide 400 ft by 4 sides.
2007-04-10 14:27:17 · answer #1 · answered by Philippe 3 · 0⤊ 0⤋
Make a square pen, remember a square is a rectangle! The pen would have side measuring 100 ft ( 4 sides so there is your 400 ft)
Area is L x W
= 100 by 100
= 10,000 sq ft
2007-04-10 21:30:30 · answer #2 · answered by Critters 7 · 0⤊ 0⤋
The perimeter of the fence will be 2*l + 2*w = 400
The area is A = l*w. You want to maximize the area. So, solve your perimeter equation for either l or w.
w = 200 - l
Plug this in for w in the area equation and take the derivative of A with respect to l and set it equal to 0. Solve for l.
A = l * (200 - l) = 200l - l^2
A' = 200 - 2l
200 - 2l = 0
l = 100.
You can now solve for w.
w = 200 - l
w = 100, so the dimensions are 100x100.
2007-04-10 21:30:08 · answer #3 · answered by Michael 2 · 0⤊ 0⤋
The rectangle with the largest area for a given perimeter is a square. So he should make a 100 by 100 foot square.
The figure that would give the largest possible area for a given perimeter is a circle.
2007-04-10 21:28:03 · answer #4 · answered by Jeffrey K 7 · 0⤊ 0⤋
a 100 ft square encloses the largest area.
2007-04-10 21:27:09 · answer #5 · answered by bz2hcy 3 · 0⤊ 0⤋