Question

a triangle has two sides of lengths 5 and 12. what value could the length of the third side be? check all that apply.
a. 17
b. 5
c. 7
d. 19
e. 11
f. 9

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the sides of the triangle be \(a = 5\), \(b = 12\), and \(c\) be the third - side. Then \(a + b>c\), \(a + c>b\), and \(b + c>a\). Also, \(|a - b|

Step2: Calculate the range of the third - side

We know that \(|5 - 12|=7\) and \(5 + 12 = 17\). So, \(7

Answer:

E. 11, F. 9