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30 Apr 2019, 01:25
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C
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Difficulty:
65%
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Question Stats:
61% (03:09) correct
39%
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wrong
based on 145
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A rectangular room is 12 feet long, 8 feet wide, x feet high, and has a volume of 1152 cubic feet.What is the greatest distance (in feet) between the center of the ceiling and any other point in the room?
A. \(8 \sqrt{2}\)
B. 12
C. 14
D. \(12 \sqrt{2}\)
E. 20
A. \(8 \sqrt{2}\)
B. 12
C. 14
D. \(12 \sqrt{2}\)
E. 20
01 May 2019, 01:50
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Bunuel
GMATinsight ; sir how to calculate the greatest distance (in feet) between the center of the ceiling and any other point in the room?
diagonal midpoint at top is to be considered but how to determine greatest distance , the shape will be like a pyramid i think.
01 May 2019, 02:59
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Bunuel
L = 12
B = 8
H = x
Volume = L*B*H \(= 12*8*x = 1152\)
i.e. \(x = 12\)
The Center of the ceiling is at a height of 12 feet from the floor (DROP a perpendicular from center of the ceiling on the floor) Let's say Point P
Join the P point obtained at floor with the corner of the floor, the length of this line \(= (\frac{1}{2})*√(12^2+8^2) = √52\) (Half of the diagonal of the rectangular floor)
Join Center of the ceiling Point with the same corner of the floor (The Longest distance to be calculated RED LINE)
Now we have the triangle and the Line joining the the center of the ceiling with corner of the floor is the longest distance
Distance \(= √[12^2 + (√52)^2] = √196 = 14\)
Answer: Option C
Archit3110
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