Hello, Kali!

A rectangular swimming pool is to be built with an area of 1800 ft².

The owner wants 5-ft wide decks along either side and 10-ft wide decks at the two ends.

Find the dimensions of the smallest piece of property on which this pool can be built. Code:

: 10 : - - - L - - - : 10 :
- * - - * - - - - - - - * - - * -
5 | | :
- * * - - - - - - - * * :
: | | | | :
: | | | | :
W | | W | | W+10
: | | | | :
: | | L | | :
- * * - - - - - - - * * :
5 | | :
- * - - * - - - - - - - * - - * -
: - - - - - L+20 - - - - - :

The dimensions of the pool are by

The area of the pool is 1800 ft²: . .[1]

The total area has dimensions by

We have: . .[2]

Substitute [1] into [2]: .

. . which simplifies to: .

Differentiate and equate to zero: .

Multiply by

. . Hence: .

Substitute into [1]: .

Therefore, the property will be: .