Posted by **Shadow** on Thursday, December 1, 2011 at 10:34pm.

A gardener is putting a wire fence along the edge of his garden to keep animals from eating his plants.

-If he has 20 meters of fence, what is the largest rectangular area he can enclose?

-What quadratic function represents the area of the garden?

Thanks

- Algebra -
**tchrwill**, Friday, December 2, 2011 at 11:02am
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.

Given 20 meters of fence, the garden is 5 x 5.

*--Considering all rectangles with the same area, the square results in the smallest perimeter for a given area.

*--Given a fixed length of fence, the circle encloses the maximum area.

## Answer this Question

## Related Questions

- Math - A gardener is putting a fence along the edge of his garden. If he has 20 ...
- Math - 1. A gardener has 140 feet of fencing to fence in a rectangular vegetable...
- algebra - Maria’s garden has 24 meters of fence and she wants to fence the ...
- engineering mathematics 1 - your father wants to fence a rectangular area in ...
- Geometry - Harris is planting a rectangular garden with an area of 48 square ...
- word problems - harris is planting a rectangular garden with an area of 24 ...
- Algebra - A farmer has 230 ft of fence to enclose a rectangular garden. What is ...
- Math - A rectangular garden is surrounded by a roll of chicken wire fencing to ...
- Math - The Maximum Garden Problem. A farmer has 230 ft of fence to enclose a ...
- Algebra - a rectangular garden is located adjacent to a house the family needs ...