Question

A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the​ width, find the dimensions of the pool.

Answer 1

`x \approx 21.080\,ft`,
`y = 29.080\,ft`

Explanation:

The total area of the pool and the walkway is:

`(x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^(2)`

`(x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^(2)`

`x^(2) + 20\cdot x + 84\,ft^(2) = 950\,ft^(2)`

`x^(2) + 20\cdot x - 866\,ft^(2) = 0`

The roots of the second-order polynomial is:

`x_(1) \approx 21.080\,ft` and
`x_(2) \approx -41.081\,ft`

The only possible root is:

`x \approx 21.080\,ft`

The other dimension of the pool is:

`y = x + 8\,ft`

`y = 21.080\,ft + 8\,ft`

`y = 29.080\,ft`