Sunday

April 20, 2014

April 20, 2014

Posted by **Anonymous** on Thursday, November 3, 2011 at 11:02am.

- geometry -
**Reiny**, Thursday, November 3, 2011 at 12:37pmnot much of a problem here ...

the largest rectangle is obtained when that rectangle is a square, so

4 equal sides equal 32 feet,

each side is 8 feet

area is 64 square ft

- geometry -
**tchrwill**, Friday, November 4, 2011 at 10:52amConsidering all rectangles with a given perimeter, which one encloses the largest area?

The traditional calculus approach would be as follows.

Letting P equal the given perimeter and "x" the short side of the rectangle, we can write for the area A = x(P - 2x)/2 = Px/2 - x^2.

Taking the first derivitive and setting equal to zero, dA/dx = P/2 - 2x = 0, x becomes P/4.

With x = P/4, all four sides are equal making the rectangle a square.

.....The short side is P/4.

.....The long side is (P - 2(P/4))/2 = P/4.

Therefore, it can be unequivicaly stated that of all possible rectangles with a given perimeter, the square encloses the maximum area.

**Related Questions**

Geometry - given 18 feet of fencing what is the largest area that you can ...

Geometry - given 18 feet of fencing what is the largest area that you can ...

geometry - a school playground is in the shape of a rectangle 500 feet long and ...

Geometry - Jose wants to put fencing around his rectangular garden. His garden ...

math - Robbie needs to buy fencing for his square vegetable garden that measures...

math - Yolanda is putting up a fence for her dog in the shape of a square. Each ...

math - company A:1/5 company B:4/25 company C:2/5 company D:3/20 Fencing 40 1/2 ...

Math - Two of the local ranchers are bragging about their ability to use fencing...

College Algebra - Rita has 88 feet of fencing. She wants to use this fencing to ...

Algebra - A builder has 80 feet of fencing to create an enclosure adjacent to a ...