Question

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

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

Answer 1

Option (C) is correct.

The range of the possible values of x is 4< x <14.

Explanation:

Given : a triangle with side length of 5 feet , 9 feet and x feet.

We have to find the possible range of x,

The range of possible lengths of a side depends on the lengths of the other two sides.

The length of side x must be less than the sum of the other two sides.

⇒ Here, x < 9+5, or x < 14.

Also, the length of side x must be greater than the difference of the other two sides.

⇒ Here, x > 9 -5 , or x > 4.

Thus, we have the range for the possible values of x that is 4< x < 14

Thus, option (C) is correct.

Answer 2

The best and most correct answer among the choices provided from your question about the triangle is the third choice or letter C. 4 < x < 14. The solution for the answer is as follows:

9-5 = 4
9+5 = 14

Therefore, 4<x<14

I hope that helps you.