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) (Show Source): You can put this solution on YOUR website!
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
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