two sides of a triangle have lengths 8 and 17. which inequalities represent the possible lengths for the third side, x?
a. 9<x<17
b. 9<x<8
c. 8<x<17
d. 9<x<25
The length of any side of a triangle must be shorter than the sum of the lengths of the other two sides and longer than the difference between the lengths of the other two sides.
In this case, the lengths of the two given sides are 8 and 17.
So, the possible lengths for the third side, x, can be represented by the inequality:
|17 - 8| < x < 17 + 8
Simplifying this inequality gives:
9 < x < 25
Therefore, the correct answer is d. 9 < x < 25.