Rectangular & Circular Swimming Pools

[nycmathguy]

College Algebra
Chapter 3

 

[MathLover1]

rectangular-shaped pool:
p=1000ft

p=2(a+b)=1000-> a+b must be 500,

so, experiment what length and the width are the best choice for pool

let a=300 and b=200
the area would be 300*200=60000ft^2

let a=400 and b=100
the area would be 400*100=40000ft^2

or
let a=450 and b=50
the area would be 450*50=22500ft^2

from experiment above, the best choice is: a=300ft and b=200ft because the area will be greatest

circular pool:

perimeter is 1000ft
p=2rpi
1000ft=2r*pi
500ft=r*pi
r=500ft/pi
r=159.16ft

then the area will be:

A=(159.16ft)^2*pi
A=79580 ft^2

as you can see, you should build a circular pool because it will have greater area than rectangular-shaped pool

 

[nycmathguy]

rectangular-shaped pool:
p=1000ft

p=2(a+b)=1000-> a+b must be 500,

so, experiment what length and the width are the best choice for pool

let a=300 and b=200
the area would be 300*200=60000ft^2

let a=400 and b=100
the area would be 400*100=40000ft^2

or
let a=450 and b=50
the area would be 450*50=22500ft^2

from experiment above, the best choice is: a=300ft and b=200ft because the area will be greatest

circular pool:

perimeter is 1000ft
p=2rpi
1000ft=2r*pi
500ft=r*pi
r=500ft/pi
r=159.16ft

then the area will be:

A=(159.16ft)^2*pi
A=79580 ft^2

as you can see, you should build a circular pool because it will have greater area than rectangular-shaped pool

I like your reasoning to the answer. By "experiment" you mean trial and error, yes? Mira, you are ready to be a construction worker. I like swimming pools regardless of shape. The deep end is my favorite. Do you know how to swim? Do you prefer the shallow end or deep end with diving board?

 

[MathLover1]

yes, by "experiment" I mean trial and error
I am very familiar with construction work, actually my sons renovated our home after flood back in 2010.
this is how it was:

But my hobby is painting. I hope you see some of my paintings on the wall.

 

[nycmathguy]

yes, by "experiment" I mean trial and error
I am very familiar with construction work, actually my sons renovated our home after flood back in 2010.
this is how it was:

But my hobby is painting. I hope you see some of my paintings on the wall.

I will watch the clip later on.my break. Thanks for sharing. Sorry this happened to you.