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The lengths of two sides of a certain obtuse triangle are 9

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The lengths of two sides of a certain obtuse triangle are 9

by Max@Math Revolution » Thu Aug 09, 2018 12:20 am

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[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
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For obtuse angle $$a^2+b^2 < c^2$$

by swerve » Fri Aug 10, 2018 9:45 am
For obtuse angle
$$a^2+b^2 < c^2$$
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by Max@Math Revolution » Mon Aug 13, 2018 5:11 am
=>


If a, b and c are sides of a right triangle and c is the longest side, then c^2 = a^2 + b^2.
If a, b and c are sides of an acute triangle and c is the longest side, then c^2 < a^2 + b^2.
If a, b and c are sides of an obtuse triangle and c is the longest side, then c^2 > a^2 + b^2.

Since 15^2 = 9^2 + 12^2 and 16 > 15, 16 could be the third side of the obtuse triangle.

Therefore, the answer is E.

Answer : E
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