SOLUTION: A pool measuring 8 meters by 20 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 864 square​

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Question 1016029: A pool measuring 8 meters by 20 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 864 square​ meters, what is the width of the​ path?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A pool measuring 8 meters by 20 meters is surrounded by a path of uniform​ width, as shown in the figure.
If the area of the pool and the path combined is 864 square​ meters, what is the width of the​ path?
:
let x = the width of the path
The overall dimensions is found by adding 2x to the length and width of the pool
Therefore the area:
(2x + 8) * (2x + 20) = 864
FOIL
4x^2 + 40x + 16x + 160 = 864
Combine like terms
4x^2 + 56x + 160 - 864 = 0
4x^2 + 56x - 704 = 0
simplify divide by 4
x^2 + 14x - 176 = 0
you can use the quadratic formula a=1; b=14; c=-176. But this will factor to
(x + 22)(x - 8) = 0
the positive solution is all we want here
x = 8 meters is width of the path
:
:
:
See if that checks out
(16 + 8)(16 + 20) = 864