Answer:
Option C. [tex]17\ cm[/tex]
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
so
Let
c------> the length of the third side
case 1)
[tex]5+c> 7[/tex]
[tex]c>7-5[/tex]
[tex]c>2\ cm[/tex]
case 2)
[tex]5+7> c[/tex]
[tex]12> c[/tex] ------> rewrite
[tex]c<12\ cm[/tex]
The solution of the third side is the interval-------> [tex](2,12)[/tex]
therefore
[tex]17\ cm[/tex] can not be a measure of the third side
