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I have 24 feet of fencing with which to build a rectangular rabbit pen to keep rabbits.
If I want the rabbits to have as much room as possible, how long would each of the sides be?
How long would each side be if I had only 16 feet of fencing?
How would you determine the pen with the most room for any amount of fencing?
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A rectangle with the fixed perimeter which has the maximal area is a square.
Therefore, for the first case (24 feet of fencing) the maximal area is provided by a square with the side measure
of = 6 ft and the area of 36 ft^2.
For the second case (16 feet fencing) the maximal area is provided by a square with the side measure
of = 4 ft and the area of 16 ft^2.
For the third case/question, take the length of the fencing, divide it by 4 and get the side measure
of the square, which will give you the maximal area.
All question are answered.
See the lesson
- A rectangle with a given perimeter which has the maximal area is a square
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Finding minimum/maximum of quadratic functions".