Answer:
The range of possible measures for the third side are 6 < x < 64.
Step-by-step explanation:
The sum of two sides of a triangle is always greater than the third side.
The two sides of a triangle are:
A = 35
B = 29
Suppose the third side is, C = x.
Then,
A + B > C
⇒ 35 + 29 > x
⇒ 64 > x
⇒ x < 64
But for the inequality theorem to be consistent for all the three sides, the third side must have a lower bound.
The difference between the two provided side is,
Diff = 35 - 29 = 6
The third side should not be less than 6 for the inequality theorem to hold.
Thus, the range of possible measures for the third side are 6 < x < 64.
