Question 1177833
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A landscape architect is planning a circular flower bed that will be surrounded by a ring of paving
stones, 25 cm wide. The area of the ring of paving stones will be half the area of the flower bed.
Determine the radius of the flower bed, to the nearest centimetre.
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        The solution by @mananth is incorrect due to arithmetic errors on the way.

        I came to bring a correct solution.



<pre>
pi*(r+25)^2 - pi*r^2 = (1/2)*pi*r^2


Cancel pi in both sides


(r+25)^2 - r^2 = (1/2)*r^2


r^2 + 50r + 625 - r^2 = (1/2)*r^2


50r + 625 = (1/2)r^2


r^2 - 100r - 1250 = 0


Use the quadratic formula and find  r = {{{50 +- 25*sqrt(6)}}}.


It gives a unique meaningful positive solution x = {{{50 + 25*sqrt(6)}}} = 111 cm, rounded.    <U>ANSWER</U>
</pre>

Solved.