Friday

August 29, 2014

August 29, 2014

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

-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 11:02amConsidering 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.

**Related Questions**

Math - A gardener is putting a fence along the edge of his garden. If he has 20 ...

Math - Amandeep decides to grow a vegetable garden. She wants to make it 10.1m ...

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 ...

math - Ryans mother has a fenced rectangle garden that measures 15 meters x 10 ...

college algebra word problem - Here's the problem I was asked: You are visiting ...

Maths - Chris wants to put a concrete path and a fence around his rectangular ...

Algebra - a rectangular garden is located adjacent to a house the family needs ...

maths - Chris wants to put a concrete path and a fence around his rectangular ...

4th grade - bertrand is building in the form of a rectangle. he knows that the ...