Given:
The lengths of two sides of an isosceles triangle are 5 and 9.
The objective is to find the length of third side.
Since we are given an isosceles triangle then the third side can be either 5 or 9 and it must satisfy the inequality given below, that is:
[tex]|a-b|Where a, b and c are the sides of triangle.
Now according to the question, let a= 9 and b=5
Case 1: c = 5
Substitute this in the inequality, we get:
[tex]\begin{gathered} |9-5|<5<|9+5| \\ 4<5<14 \end{gathered}[/tex]
This is true so c can be 5.
Case 2: c = 9
Substitute this in the inequality, we have:
[tex]\begin{gathered} |9-5|<9<|9+5| \\ 4<9<14 \end{gathered}[/tex]
This is also true for c= 9
Hence, the third side can be either 5 or 9.
Thus, option A is true.
