Question

Triangle ABC is an acute triangle. Two sides measure 5 and 7. What is the range of possible values for its third side?

Answer 1

Answer:

the desired range is 2 < t < 12.

Step-by-step explanation:

If the third side is 12 (the sum of 5 and 7), we don't really have a triangle, since the 5-unit and 7-unit sides add up to 12 and lie on the third side (of length 12).

Since triangle ABC is acute, all its angles are between 0 and 90 degrees.  So the third side can be 12 but not greater.  The smallest possible length of the third side is 2, since 5 + 2 = 7.

Thus, the desired range is 2 < t < 12.