Question 2586: A circular pond has a diameter of 2.5 meters. The owner wants to put a concrete walkway around the pool that has uniform width. She has enough to cover 5m(squared). What is the maximum width her walkway can be?
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! If the width of the walkway is x meters, then its area is
pi(x + 2.5/2)^2 - pi (2.5/2)^2 = pi(x^2 + 2.5 x)
Solve: pi(x^2 + 2.5 x) <= 5,
or x^2 + 2.5 x - 5/pi <= 0
use pi = 3.1416 and quadratic formula,
two roots of x^2 + 2.5 x - 5/pi = 0 are
0.525963319, -3.025963319
when x is between these two roots, x^2 + 2.5 x - 5/pi <= 0
but x width shouldbe > 0.
Hence,x <= 0.5259 meters... max possible value of width
Kenny
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