Engineering
posted by Alexander
4. A rectangular enclosure is formed by using 800m of fencing. Find the greatest possible area that can be enclosed in this way and the corresponding dimensions of the rectangle.

Damon
4 x = 800
x = 200 feet on a side square
=========================
prove that square is max area
A = x y
P = 2 x + 2 y perimeter
so x + y = P/2
A = x (P/2  x) = x^2 +P/2 x
x^2  (P/2) x = A find vertex,complete square
x^2  (P/2)x + P^2/16 = A + P^2/16
(xP/4)^2 = (AP^2/16)
vertex at x= P/4 (then y = P/4 too :)
A = (P/4)^2
so square with side = Perimeter/4 is max area
Respond to this Question
Similar Questions

geometry
a field bounded on one side by a river is to be fenced on three sides to form a rectangular enclosure. there are 320 ft of fencing available. what should the dimensions be to have an enclosure with the maximum possible area? 
Algebra 2
A rectangular field is to be enclosed by 300 feet of fencing. Find the dimensions of the enclosure that maximizes the area. 
Calculus
A construction company wants to build a rectangular enclosure with an area of 1000 square feet by fencing in three sides and using its office building as the fourth side. Your objective as supervising engineer is to design the enclosure … 
Math
Find the Dimensions of a rectangular garden of the greatest area that can be enclosed in 40 feet of fencing. 
Math
A rancher has 220 feet of fencing to enclose a rectangular corral. Find the dimensions of the rectangle that maximize the enclosed area, using all 220 feet of fencing. Then find the maximum area. 
Math
A rectengular area is to be enclosed on three sides by fencing, an existing hedge forming the fourth side. Find the greatest area of the rectangle and its dimensions if 140mof fencing is available. 
Algebra
To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 120 ft. of fencing material. a. What quadratic function represents the area of the rectangular enclosure, … 
Optimization Calculus
A three sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. There is 96 ft of fencing available. Find the maximum enclosed area and the dimensions of the corresponding … 
Maths
You have 400 meters of fencing to use to make a rectangular enclosure. Give a detailed explanation of the different dimensions and areas that you are able to create using the set amount of fencing that you have. You may also show the … 
Algebra
A rectangular pig pen is made of 84 meters of fencing on three sides. The fourth side is a barn wall. Find the dimensions and greatest possible area of the enclosure.