Posted by **alex** on Monday, October 5, 2009 at 4:33pm.

faye has 20 feet of fencing to make a rectangular pen for her dog.What is the largest area she can fence in?

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**alex**, Monday, October 5, 2009 at 4:34pm
20 feet

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**alex**, Monday, October 5, 2009 at 4:38pm
is that right im just gessing

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**Ms. Sue**, Monday, October 5, 2009 at 4:39pm
Let's see --

it could be 5 + 5 + 5 + 5

or 4 + 4 + 6 + 6

or 3 + 3 + 7 + 7

Find the areas of these pens.

A = length times width

So -- a 3 foot by 7 foot pen would be 21 square feet.

Find the areas of the other two pens. Which gives you the most square feet?

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**MathMate**, Monday, October 5, 2009 at 4:39pm
For a math question:

Make a table of width (W) and lengths (L) that add up to 20 for perimeter = 2(W+L).

Calculate the area for each line. Choose the biggest area.

Width Length Area

1 9 9

2 8 16

3 7 21

4 6 24

.....

8 2 16

9 1 9

For a calculus question:

Let W=width, then

(10-W)=length, and

Area=A(W)=W(10-W)=10W-W²

For maximum or minimum:

dA/dW=10-2W=0, or W=5

d²A/dW²=-2 <0 so maximum.

A(5)=5(10-5)=25 (maximum area)

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**alex**, Monday, October 5, 2009 at 5:15pm
hi im only in 4th grade so i really kind of need simple answers

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**Ms. Sue**, Monday, October 5, 2009 at 5:27pm
Please see my answer. I'm sure you can figure out your answer using that information.

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**alex**, Monday, October 5, 2009 at 5:28pm
thanks ms.sue u rock

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**Ms. Sue**, Monday, October 5, 2009 at 5:30pm
You're welcome, Alex. :-)

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