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Nabu's Knee-knocker
Background
| Perhaps you know that the largest (in area) rectangle
with perimeter 120 meters is a square with 30 meter
sides. The area is 900 square meters (m2).
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You can check the area of other rectangles with perimeter 120 meters.
So, if you have 120 meters of fencing to build a rectangular pen and
you want the pen to have as large an area as possible, you'd make
a square pen with 30 meter sides.
Problems
| Suppose you have 120 meters of fencing and want to
build two congruent rectangular pens with one side in common.
Congruent means the rectangular pens look exactly alike.
The picture shows an example. |
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Also, suppose you want the total area to be as large as possible.
What dimensions do you make the rectangular pens?
- Consider the same problem for making three or four rectangular
pens with 120 meters of fencing.
What dimensions do you make the rectangular pens?
- Can you describe how to build several rectangular pens
(any number) with 120 meters of fencing and with as large a total
area as possible?
You may want to print this page and do your
work in the blank space below.
Scroll down the page to find a hint and the
solution to this problem.
Are you stumped? Do you need a hint? If so, click the Hint
button.
Do you think you've figured out all the solutions? If so, then click
the Solution button.
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