Chapter A.2, Problem 57AYU

To determine

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 objective is to have a pool that encloses the most area, what shape should you use?

Answer to Problem 57AYU

Circular type pool.

Explanation of Solution

Given:

You have 1000 feet of flexible pool siding and intend to construct a swimming pool. Experiment with rectangular- shaped pools with perimeters of 1000 feet.

Calculation:

Given, the circumference of the rectangular pool is 1000 feet.

$2\left(l+w\right)=1000$

$l+w=500$

Possibly $l=250$ and $w=250$.

Area of the rectangular pool is $=l\times w\approx 62500$ feet.

Given, the circumference of the circular pool is 1000 feet.

$2\pi r=1000$

$r=159.16$

Area of the circular pool is $=\pi r^2\approx 79577$ feet.

I suggest circular type pool.