Question

Two sides of a triangle have lengths 14 and 25 . The length of the third side can be any number between

a. 11 and 14
b. 14 and 39
c. 14 and 25
d.11 and 39
e. None of the above

Answer 1

The length of the third side of a triangle must be between 14 and 39.

Step-by-step explanation:

The length of the third side of a triangle can be determined by the triangle inequality theorem. According to this theorem, the length of the third side must be greater than the difference of the lengths of the other two sides, and less than the sum of their lengths.

In this case, the lengths of the two sides are 14 and 25. Therefore, the third side must be greater than |25 - 14| = 11, and less than 25 + 14 = 39.

So, the correct option is b. 14 and 39.