The short answer:
Subtract the two given sides.
Add the two given sides.
The third side can be any number IN BETWEEN these values.
#1
12, 10
12-10 = 2
12+ 10 = 22
your missing side can be anything between 2 and 22
written in the form of an inequality:
2 < x < 22
#2
12.7
12-7 = 5 and 12+7 = 19
third side can be 5 < x < 19
#3
8,12
12-8 = 4 and 12+8 = 20
third side can be 4 < x < 20
#4
9,9
9-9 = 0 and 9+9 = 18
third side can be 0 < x < 18
#5
10,9
10-9 = 1 and 10+9 = 19
third side can be 1 < x < 19
#6
12,9
12-9 = 3 and 12+9 = 21
third side can be 3 < x < 21
#7
6,11
11-6 = 5 and 11+6 = 17
third side can be 5 < x < 17
#8
11,12
12-11 = 1 and 12+11 = 23
third side can be 1 < x < 23
#9
9,8
9-8 = 1 and 9+8 = 17
third side can be 1 < x < 17
#10
7,11
11-7 = 4 and 11+7 = 18
third side can be 4 < x < 18
Hope this clears it up!
*note: if the two small sides don’t add up to more than the biggest side, you can’t make a triangle (the sides won’t be able to reach each other*
That is the concept that this homework is teaching -> your two small sides always have to add up to more than the biggest side
