SOLUTION: The measures of two sides are given. Between what two numbers must the third side fall? Given: 9 and 15 (Write an inequality to represent your answer)

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Question 1191826: The measures of two sides are given. Between what two numbers must the third side fall?
Given: 9 and 15 (Write an inequality to represent your answer)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

The third side must be between the numbers 15-9 = 6 and 15+9 = 24


    6 < c < 24.      ANSWER

Solved.

It follows from the triangle inequalities.




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


TRIANGLE INEQUALITY: The length of the longest side of a triangle must be less than the sum of the lengths of the other two sides; otherwise a triangle can't be formed.

(1) If the 9 and 15 are the two shorter sides, the third side must be less than 9+15 = 24 to make a triangle.

(2) If 15 is the longest side and one of the other sides is 9, then the long side is 6 longer than that other side, so the length of the third side must be greater than 6 for the three lengths to make a triangle.

ANSWER: The length of the third side must be greater than 6 and less than 24.