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

[Max@Math Revolution]

[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

[swerve]

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

[Max@Math Revolution]

=>


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