Answers:
6 inches = yes
12 inches = yes
22 inches = no
5 inches = no
14 inches = yes
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Explanation:
Let,
a = length of XY = 8 inches
b = length of YZ = 13 inches
c = length of XZ = unknown
By the triangle inequality theorem, we can say
b-a < c < b+a
13-8 < c < 13+8
5 < c < 21
So the segment XZ can be any length between 5 and 21, but it cannot be 5 or it cannot be 21.
From the given answer choices, the possible values for XZ are: 6, 12 and 14.
The values of 22 and 5 are outside the interval 5 < c < 21, so those lengths are not possible for XZ.
