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An accurate answer requires elliptical integrals which is probably beyond the ability of many students with a university degree in mathematics!

A reasonably good approximation, due to Ramanujan, is

pi*[3*(a + b) - sqrt(10*a*b + 3*(a2 + b2)]

where a is the semi major axis = 24/2 = 12 feet

and b is the semi minor axis = 16/2 = 8 feet.

This gives P = 63.46 ft.

A quick an dirty way is as follows:

A circular pool of 16' diameter would have a perimeter of 16*pi = 50.27 ft

One with a 24' diameter would have a perimeter of 24*pi = 75.40 ft

The oval one would be roughly halfway between = 62.8 ft.

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Q: What is the circumference of a 16x24 oval pool?
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