5
QuizMultiple Choice

Triangle Inequalities

Question 5 • Q5 Geometry New 2022

If a triangle has side lengths of 5 feet, 9 feet, and x feet, find the range of possible values of x.

Answer
A
0 < x < 14
B
4 < x < 9
C
4 < x < 14
D
5 < x < 9

Explanation

For three lengths to form a triangle, the third side must be greater than the difference of the other two sides and less than their sum. Here, |9 − 5| < x < 9 + 5, so 4 < x < 14. The correct choice is C, 4 < x < 14.

AI-written and checked against the verified answer.

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