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

`c = 11`

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