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John wants to construct a circular swimming pool in his plot which is

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New post 25 Nov 2019, 01:06
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Difficulty:

  45% (medium)

Question Stats:

53% (01:16) correct 47% (02:45) wrong based on 17 sessions

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John wants to construct a circular swimming pool in his plot which is in the shape of a trapezium. The lengths of the oblique sides of the plot are 26 m and 30 m. If the radius of the biggest circle that can be marked for the pool is 12 m, what must be the minimum area (in sq.m) of the plot?

(A) 336
(B) 672
(C) 728
(D) 1344
(E) 1400
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John wants to construct a circular swimming pool in his plot which is  [#permalink]

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New post 25 Nov 2019, 09:03
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CaptainLevi wrote:
John wants to construct a circular swimming pool in his plot which is in the shape of a trapezium. The lengths of the oblique sides of the plot are 26 m and 30 m. If the radius of the biggest circle that can be marked for the pool is 12 m, what must be the minimum area (in sq.m) of the plot?

(A) 336
(B) 672
(C) 728
(D) 1344
(E) 1400


Perhaps there is a better way to solve this to get the accurate answer but here is one logic :

The area of the trapezium cannot possibly be lesser than circle which is to be made within it.
Area of the circle with radius=12, \(\pi*12^2 = 452.16\), hence minimum area of the plot must be more than 452.16. Among the answer choices , just above 452.16 is 672 , Hence B seems possible.

Ans- B
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John wants to construct a circular swimming pool in his plot which is   [#permalink] 25 Nov 2019, 09:03
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