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 970 ft2. If the length of the pool is 8 feet longer than the? width, find the dimensions of the pool. The length of the pool is nothing feet and the width is nothing feet.

Answer 1

Answer:

29.4 length and 21.4 width.

Step-by-step explanation:

To fin the dimensions of the pool we need to use the total area of the pool plus the concrete walkway. Lets say that W is the width and L the length. We know that, the walkway has 3 ft wide, this means that the width and length are increased by 6ft (3ft on each side). So, the total area can be expressed like this:  $A_{total} = (L+6)(W+6)$.

In addition, we know that the total area is 970 and the length is 8 ft longer than the width ($L=W+8$). So:

$A_{total} = (L+6)(W+6)\\970 = (W+8+6)(W+6)\\970=W^{2}+20W+84\\W^{2}+20W-886=0$

With this quadratic equation we're gonna have to solution, the most reasonable is part of the answer. So, solving the equation we have as solutions: $W_{1}=21.4$ and  $W_{2}=-41.4$

Therefore, the width is 21.4 ft, because the negative number cannot represent distances.

Using the relation between length and width:

$L=W+8\\L=21.4+8=29.4$

Therefore, the dimensions of the pool are 29.4 length and 21.4 width.