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

Answer:

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

Step-by-step 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:

$y = x + 8\,ft$

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

$y = 29.080\,ft$