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44 votes
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.

User Akobold
by
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1 Answer

7 votes
7 votes

Answer:


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

User Sushil Bansal
by
2.7k points