SOLUTION: A small square pool is surrounded by a concrete walk two meters wide. If the area of the pool is 2/3 of the total area of the pool and the walk, find the outer dimensions of the wa
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Question 785392: A small square pool is surrounded by a concrete walk two meters wide. If the area of the pool is 2/3 of the total area of the pool and the walk, find the outer dimensions of the walk.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= outer side of the concrete walk (in meters)
Since there are meters of concrete walk to either side of the pool, the length of one side of the pool,
= length of the side of the pool (in meters).
= total area of the pool plus concrete walk (in square meters)
area of the pool (in square meters).
What the problem says in words translates as
Multiplying times 3 both sides of the equation, we get
SOlving that quadratic equation, we get two solutions.
One is negative, which does not make sense.
The other one is
The outside dimensions of the walk are 21.8 meters by 21.8 meters.
(The pool sides measure 21.8 meters - 4 meters = 17.8 meters).
SOLVING THE QUADRATIC EQUATION:
Using the quadratic formula:
Completing the square:
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