Question

A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5- foot wide decks along the two sides and 10-foot wide decks at the two ends. Find the dimensions of the smallest piece of land on which the pool (including the decks) can be built satisfying these conditions.

Answer 1

Answer:
`y = 20√(15)feet`,
`x = 10√(15)feet`

Explanation:

given data:

area of the pool = 1800 square feet.

length along the deck = 5- foot

length of side along the deck = 10-foot

Solution:

dimension of the pool =
`x * y`

total area
`A = (20+y)(10+x)`
`...................eqn1`

since
`xy = 3000\\`

`y = (3000)/(x)`
`..............................eqn2`

insert eqn2 into eqn1

`A = ((3000)/(x) +20)(10+x)`

`A = (3000(x+10))/(x^(2) ) + (3000)/(x) +20`

`20 - (30000)/(x^(2) ) = 0`

`x = 10√(15)`feet

to solve for y,
`(60000)/(x^(3) )`

`y = 20√(15)`