SOLUTION: There is a pool with a cement walkway around it. The pool measures 6 meters by 10 meters and the total area of the pool is 96 meters. Find the width of the walkway

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Question 624813: There is a pool with a cement walkway around it. The pool measures 6 meters by 10 meters and the total area of the pool is 96 meters. Find the width of the walkway
Answer by nerdybill(7384) (Show Source):
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There is a pool with a cement walkway around it. The pool measures 6 meters by 10 meters and the total area of the pool is 96 meters. Find the width of the walkway
.
Let w = width of walkway
then
"area of pool & walkway" - "area of pool" = 96
(6+2w)(10+2w) - (6)(10) = 96
60+12w+20w+4w^2 - 60 = 96
60+32w+4w^2 - 60 = 96
32w+4w^2 = 96
4w^2+32w = 96
4w^2+32w-96 = 0
w^2+8w-24 = 0
applying the quadratic formula yields:
w = {-10.32, 2.32}
we can throw out the negative solution leaving:
w = 2.32 meters
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=160 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.32455532033676, -10.3245553203368. Here's your graph: