Question

there is a pool of radius x and there is a pathway around the pool with a width of 4 feet. find the radius of the pool if the path area/ pool area = 11/25. 1) 12 2) 20 3) 25 4) 29

Answer 1

the radius of the pool be x.
Then area of the wall and pool = π(x + 4)²

Area of the pool = πx²

Area of the wall = area of wall and pool - area of pool

GIVEN:-
area of wall/area of pool = 11/25
so, area of wall = 11/25 * area of pool

therefore, 11/25πx² = π(x + 4)² - πx²

π(x² + 16 + 8x - x²) = 11/25πx²

(16 + 8x) = 11/25x²

25(16 + 8x) = 11x²

400 + 200x = 11x²

11x² - 200x - 400 = 0

11x² - 220x + 20x - 400 = 0

11x(x - 20) + 20(x - 20) = 0

(11x + 20)(x - 20) = 0

Hence, x = 20 , x = -11/20[x can't be negative]


Hence, option ( 2 ) is correct


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THANKS

Answer 2

Answer:

20is correct

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