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meriva
4 years ago
10

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.
Mathematics
1 answer:
Sloan [31]4 years ago
3 0

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

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