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The greatest possible whole-number length of the unknown side among the option is 9 inches.
Obtuse triangle is a triangle that has one of it internal angle greater than 90 degrees.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
If the sides of the triangles are x, y and z. Therefore,
x + y > z
x + z > y
y + z > x
Therefore, the greatest possible length among the option is 9.
Proof
12 + 14 > 9
12 + 9 > 14
14 + 9 > 12
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