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18 Aug 2015, 09:59
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
83% (01:06) correct
17%
(01:04)
wrong
based on 731
sessions
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Which of the following groups of numbers could be the lengths of the sides of a right triangle?
I. 1, 4, \(\sqrt{17}\)
II. 4, 7, \(\sqrt{11}\)
III. 4, 9, 6
(A) I only
(B) I and II only
(C) I and III only
(D) II and Ⅲ only
(E) I, II and III
I. 1, 4, \(\sqrt{17}\)
II. 4, 7, \(\sqrt{11}\)
III. 4, 9, 6
(A) I only
(B) I and II only
(C) I and III only
(D) II and Ⅲ only
(E) I, II and III
ENGRTOMBA2018
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18 Aug 2015, 10:16
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Bunuel
Confirm the possibility by the formula:
(largest side)^2 = side 1^2 + side 2^2
Only (I) gives you a "yes" for the above relation and thus A is the correct answer.
\(1^2+4^2=(\sqrt{17})^2\)
but
\(4^2+6^2 \neq 9^2\) or \(4^2+(\sqrt{11})^2 \neq 7^2\)
18 Aug 2015, 20:42
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Bunuel
IMO : A
In a right triangle = a^2+b^2 = c^2 (where c is the largest side)
I. 1, 4, √17
√16 = 4. Thus √17 must be greater than 4. Thus √17 is the largest side.
(√17)^2 = (4)^2+(1)^2
Satisfies
II. 4, 7, √11
Clearly 7 is the largest side.
\((7)^2 \neq{ (4)^2 +(√11)^2 }\)
Doesn't satisfy
III. 4, 9, 6
Clearly 9 is the largest side
\((9)^2 \neq{ (4)^2 +(6)^2 }\)
Doesn't satisfy
