Determine if the given information would form a

unique triangle, many different triangles, or no triangles.
9 inches, 7 inches, 18 inches

2 answers

Mark sides as:

a = 9 , b = 7 , c = 18

Apply triangle inequality theorem:

a + b > c

b + c > a

a + c > b

This rule must be satisfied for ALL three conditions of the sides.

First condition:

a + b > c

9 + 7 > 18

16 > 18

This is obviously not true, so sides:

a = 9 , b = 7 , c = 18

cannot be sides of any triangle.
if the sides are a,b,c in increasing order, then you must have
b-a < c < b+a
for your numbers, you need
9-7 < 18 < 9+7
2 < 18 < 16
which is false, so no triangles.
Think of it. If you lay down the sides 7 and 9, they are not long enough to even cover the base of length 18, much less fold up to form a triangle.