# Algebra

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?
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1. 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.

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Question 812207: 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?
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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?
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let x=length

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