Answer:
![c = 11](https://tex.z-dn.net/?f=c%20%3D%2011)
Step-by-step explanation:
Given
Let the three sides be a, b and c
Such that:
![a = b= 5](https://tex.z-dn.net/?f=a%20%3D%20b%3D%205)
Required
Find c such that a, b and c do not form a triangle
To do this, we make use of the following triangle inequality theorem
![a + b > c](https://tex.z-dn.net/?f=a%20%2B%20b%20%3E%20c)
![a + c > b](https://tex.z-dn.net/?f=a%20%2B%20c%20%3E%20b)
![b + c > a](https://tex.z-dn.net/?f=b%20%2B%20c%20%3E%20a)
To get a valid triangle, the above inequalities must be true.
To get an invalid triangle, at least one must not be true.
Substitute: ![a = b= 5](https://tex.z-dn.net/?f=a%20%3D%20b%3D%205)
![10 > c](https://tex.z-dn.net/?f=10%20%3E%20c)
![c > 0](https://tex.z-dn.net/?f=c%20%3E%200)
![c > 0](https://tex.z-dn.net/?f=c%20%3E%200)
The results of the inequality is:
and ![c > 0](https://tex.z-dn.net/?f=c%20%3E%200)
Rewrite as:
and
![0 < c < 10](https://tex.z-dn.net/?f=0%20%3C%20c%20%3C%2010)
This means that, the values of c that make a valid triangle are 1 to 9 (inclusive)
Any value outside this range, cannot form a triangle
So, we can say:
, since no options are given