Friday

April 18, 2014

April 18, 2014

Posted by **lola** on Saturday, July 14, 2012 at 11:29am.

Thanks much!

lola

- calculus? -
**Steve**, Saturday, July 14, 2012 at 12:10pmassuming the garage will be one of the long sides (otherwise lots of extra fencing will be used), then if the long side is x, the short side will be 50/x.

So, the amount of fence, f, is

f(x) = x + 2(50/x) = x + 100/x

df/dx = 1 - 100/x^2

we want minimum fence, so df/dx = 0:

x = 10

So, the pen is 10x5, using 20 ft of fence.

Note that the square is the figure of maximum area using a given perimeter. Or, conversely, a square haas the minimum perimeter to enclose a given area.

Your pen is just two squares, where each encloses half the area. The garage wall helps out here.

**Related Questions**

evaluating a math question - a Rectanglular pen for a pet is 5 feet longer than ...

math - A FARMER BUILT A PEN FOR HIS FAVORITE PIG. THE PEN SHOWN BELOW HAS AN ...

Calculus - A rancher wants to build a rectangular pen with an area of 150 m2. ...

Calculus - A rancher wants to make a rectangular pen to house her animals. She ...

Math: Pre-calculus - A rancher wants to build a rectangular pen with an area of ...

algebra - Ian wants to build a rectangular pen for his animals. One side of the ...

math - a rectangular pen is to be constructed alongside a barn using 120 feet of...

calculus - a farmer wants to make a rectangular pen from 200 feet of fencing. he...

Calculus - A rancher wants to build a rectangular pen with an area of 150 m^2? a...

math - describe the largest pen area possible using the same amount of fencing ...