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jamesphw
Joined: 21 Nov 2013
Last visit: 18 Jun 2016
Posts: 8
Location: Canada
Concentration: Strategy, Technology
Schools: Ross '18 (M)
02 Dec 2013, 20:06
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C
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Difficulty:
25%
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Question Stats:
76% (01:55) correct
24%
(01:45)
wrong
based on 245
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Three of the sides of a rectangular prism have areas of 91, 39, and 21. What is the volume of the rectangular prism?
A) 252
B) 269
C) 273
D) 920
E) 1911
A) 252
B) 269
C) 273
D) 920
E) 1911
03 Dec 2013, 02:28
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jamesphw
Say the dimensions of the rectangular solid are a, b and c. It's volume is abc.
ab = 91;
ac = 39,
bc = 21.
Multiply these three: \((abc)^2 = 91*39*21 = (7*13)*(3*13)*(3*7) = 3^2*7^2*13^2\) --> \(abc=3*7*13=273\).
Answer: C.
General Discussion
02 Dec 2013, 22:47
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The sides are
\(\sqrt{\frac{91*21}{39}}\) = \(\sqrt{\frac{13*7*3*7}{13*3}}\) = 7
\(\sqrt{\frac{91*39}{21}}\) = \(\sqrt{\frac{13*7*13*3}{3*7}}\) = 13
\(\sqrt{\frac{21*39}{91}}\) = \(\sqrt{\frac{3*7*13*3}{13*7}}\) = 3
Volume = 13*3*7 = 273
Answer is C
\(\sqrt{\frac{91*21}{39}}\) = \(\sqrt{\frac{13*7*3*7}{13*3}}\) = 7
\(\sqrt{\frac{91*39}{21}}\) = \(\sqrt{\frac{13*7*13*3}{3*7}}\) = 13
\(\sqrt{\frac{21*39}{91}}\) = \(\sqrt{\frac{3*7*13*3}{13*7}}\) = 3
Volume = 13*3*7 = 273
Answer is C
