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09 Aug 2018, 01:33
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:29) correct
29%
(01:36)
wrong
based on 85
sessions
History
Date
Time
Result
Not Attempted Yet
[Math Revolution GMAT math practice question]
The lengths of two sides of a certain obtuse triangle are \(9\) and \(12\). Which of the following could be the length of the third side of the triangle?
\(A. 12\)
\(B. 13\)
\(C. 14\)
\(D. 15\)
\(E. 16\)
The lengths of two sides of a certain obtuse triangle are \(9\) and \(12\). Which of the following could be the length of the third side of the triangle?
\(A. 12\)
\(B. 13\)
\(C. 14\)
\(D. 15\)
\(E. 16\)
09 Aug 2018, 02:05
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MathRevolution
OA: E
For obtuse angle
\(a^2+b^2<c^2\)
As answer options are greater than or equal to sides given in question stem i.e \(9,12\). \(c\) would be the dimension of the side opposite the obtuse angle.
\(a\) and \(b\) can be either \(9\) or \(12\).
\(a^2+b^2 = 9^2+12^2=81+144 =225\)
\(c^2\) can be found out by squaring the answer option
A) 144
B) 169
C) 196
D) 225
E) 256
Only Option E satisfies \(a^2+b^2<c^2\) i.e \(225< 256\)
09 Aug 2018, 09:19
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MathRevolution
\(H = \sqrt{12^2 + 9^2}\)
Or, \(H = \sqrt{225}\)
So, \(H = 15\), Answer must be (D)
