Question

Describe lengths of three segments that could not be used to form a triangle. Segments with lengths of 5 in., 5 in., and ______ in. Cannot form a triangle.

Answer 1

Answer:

$c = 11$

Step-by-step explanation:

Given

Let the three sides be a, b and c

Such that:

$a = b= 5$

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

$a + b > c$

$a + c > b$

$b + c > a$

To get a valid triangle, the above inequalities must be true.

To get an invalid triangle, at least one must not be true.

Substitute: $a = b= 5$

$5 + 5 > c$ $===>$ $10 > c$

$5 + c > 5$  $===>$ $c > 5 - 5$ $===>$ $c > 0$

$5 + c > 5$  $===>$ $c > 5 - 5$ $===>$ $c > 0$

The results of the inequality is: $10 > c$ and $c > 0$

Rewrite as: $c > 0$ and $c < 10$

$0 < c < 10$

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:

$c = 11$, since no options are given