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**mathxyz****Member**- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 1,053

You have 1000 feet of flexible pool siding and wish to construct a swimming pool. Experiment with rectangularshaped pools with perimeters of 1000 feet. How do their areas vary? What is the shape of the rectangle with the largest area? Now compute the area enclosed by a circular pool with a perimeter (circumference) of 1000 feet. What would be your choice of shape for the pool? If rectangular, what is your preference for dimensions? Justify your choice. If your only consideration is to have a pool that encloses the most area, what shape should you use?

You say?

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,465

THis question is quite open ended with no fixed answer. With a rectangular pool you could have

eg 400 by 100

300 by 200

250 by 250

etc. Compare areas.

Algebraically We have 2(L + W) = 1000 and Area = A = LW. If you make W the subject of the first and substitute into the second you'll end up with a quadratic in L for the area. You might consider what L gives the maximum A.

But such a pool might not be best for other reasons. Could you get a good L for Olympic events? The pool I learnt to swim in had a much smaller width than length. So I could first challenge myself to do widths; then work up to lengths later.

If the pool is to be circular then you can use C = 2.pi.r to find r and hence calculate the area. Is it bigger than your best area rectangle?

Does a circle make a good pool?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathxyz****Member**- From: Brooklyn, NY
- Registered: 2024-02-24
- Posts: 1,053

Bob wrote:

THis question is quite open ended with no fixed answer. With a rectangular pool you could have

eg 400 by 100

300 by 200

250 by 250etc. Compare areas.

Algebraically We have 2(L + W) = 1000 and Area = A = LW. If you make W the subject of the first and substitute into the second you'll end up with a quadratic in L for the area. You might consider what L gives the maximum A.

But such a pool might not be best for other reasons. Could you get a good L for Olympic events? The pool I learnt to swim in had a much smaller width than length. So I could first challenge myself to do widths; then work up to lengths later.

If the pool is to be circular then you can use C = 2.pi.r to find r and hence calculate the area. Is it bigger than your best area rectangle?

Does a circle make a good pool?

Bob

1. You are right. There are no fixed answers.

2. Circular swimming pools are just as nice as rectangular pools but it all depends on the diameter of the pool.

3. I once visited Roberto Clemente Swimming Pool in the Bronx, NY. They had a circular diving pool 12 feet deep with a diameter of maybe 20 feet. I didn't like it. A good diameter for a circular pool is 35 or more feet.

4. I will go through this problem again and return here with my own conclusion.

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