# word problem: A farmer has 64 yards of fencing, and wants...

#### NFHSraider

##### New member
A farmer has 64 yards of fencing and wants to create a rectangular enclosure for his animals. what is the enclosure with the greatest area?

I need help setting the problem up.

#### tkhunny

##### Moderator
Staff member
Setup Rule Number 1 -- Name Stuff!

x = length of each of two opposite sides of the rectangle
y = length of each of the other two sides

Setup Rule #2 -- What do you know about...?

...rectangles, in this case?

2*x + 2*y = Perimeter

x*y = Area

There you have it. Now what?

#### TchrWill

##### Full Member
Re: word problem: A farmer has 64 yards of fencing, and want

NFHSraider said:
A farmer has 64 yards of fencing and wants to create a rectangular enclosure for his animals. what is the enclosure with the greatest area?

I need help setting the problem up.
Considering all rectangles with the same perimeter, the square encloses the greatest area.
Proof: Consider a square of dimensions x by x, the area of which is x^2. Adjusting the dimensions by adding a to one side and subtracting a from the other side results in an area of (x + a)(x - a) = x^2 - a^2. Thus, however small the dimension "a" is, the area of the modified rectangle is always less than the square of area x^2.