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Answer:
pool radius is 8+4√5 ≈ 16.94 meters
Explanation:
Let r represent the radius of the pool. Then r+2 is the radius to the outside of the walkway. The ratio of areas is given as 4/5, so we have ...
πr²/(π(r+2)²) = 4/5
5r² = 4(r² +4r +4) . . . . cross-multiply
r² -16r -16 = 0 . . . . . . . subtract the right-side expression from both sides
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r² -16r +64 = 80 . . . . . add 80 to complete the square
(r -8)² = 80
r -8 = √80 = 4√5 . . . . square root; use only the positive root
r = 8 +4√5 ≈ 16.94 . . . meters
The radius of the pool is 8+4√5 ≈ 16.94 meters.
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The area of a circle of radius r is given by the formula ...
A = πr²