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Answer:
[tex]c = 11[/tex]
Step-by-step explanation:
Given
Let the three sides be a, b and c
Such that:
[tex]a = b= 5[/tex]
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
[tex]a + b > c[/tex]
[tex]a + c > b[/tex]
[tex]b + c > a[/tex]
To get a valid triangle, the above inequalities must be true.
To get an invalid triangle, at least one must not be true.
Substitute: [tex]a = b= 5[/tex]
[tex]5 + 5 > c[/tex] [tex]===>[/tex] [tex]10 > c[/tex]
[tex]5 + c > 5[/tex] [tex]===>[/tex] [tex]c > 5 - 5[/tex] [tex]===>[/tex] [tex]c > 0[/tex]
[tex]5 + c > 5[/tex] [tex]===>[/tex] [tex]c > 5 - 5[/tex] [tex]===>[/tex] [tex]c > 0[/tex]
The results of the inequality is: [tex]10 > c[/tex] and [tex]c > 0[/tex]
Rewrite as: [tex]c > 0[/tex] and [tex]c < 10[/tex]
[tex]0 < c < 10[/tex]
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:
[tex]c = 11[/tex], since no options are given