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GRE - Quantitative Reasoning - Geometry

If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle?

If the lengths of two sides of a triangle are 5 and 9, respectively, which of the following could be the length of the third side of the triangle?

Indicate all such lengths.

A. 3
B. 5
C. 8
D. 15

for a triangle sum of two sides >= third side

Option check

A. 3

5 + 3 < 9.. not possible

B. 5

5 + 5 >= 9
and 9 + 5 > = 5
possible
C. 8
5 + 8 >= 9
9 + 8 > = 5
9 + 5 > = 8
possible

D. 15
9 + 5 = 14 < = 15
not possible