Question

A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5-foot wide decks along either side and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of property on which the pool can be built satisfying these conditions. Give the answers in ascending order

Answer 1

The solution would be like this for this specific problem:

A = (l + 20) · (w + 10)

The area of the pool is 1800 square feet and can be computed also like l · w. Then l · w = 1800, and therefore l = 1800 w.

We plug in the values:

A = (1800 / w + 20) · (w + 10) = 1800 + 18000 / w + 20w + 200 = 18000 / w + 20w + 2000

dA /dw = − 18000 / w2 + 20

w = 30

l = 60

Since A = (l + 20) · (w + 10):

A = (60 + 20) · (30+ 10)

A = 3,200

A(x) = 1800 + 2*10(x+10)+ 2*5(1800/x) 
= 1800 + 20x + 200 + 18000/x 
= 2000 + 20 x + 18000/x 

20 - 18000/x^2 = 0 
x = sqrt (900) = 30 
Pool length dimension = 1800/x = 60 
Lot dimensions: 80 x 40

I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.