Question

find the range for the measure of the third side of a triangle given that the measures of the other two sides are 12 and 18. how do you do this?

Answer 1

4. 10 and 12

Let side a = 10. Let side b = 12. Then the triangle
has sides

a=10, b=12, and c=?. Any side of a triangle must be less
than the other two sides added together, so

a < b+c, b < a+c, and c < a+b

Substituting:

10 < 12+c, 12 < 10+c, and c < 10+12

Solving all three for c:

-2 < c, 2 < c, c < 22

The first one is of course true, so ignore it.
Put the second and third together and get

2 < c < 22

That's it. c must be more than 2 and less than 22.
Just copy this example

Answer 2

thanks. where did you get 10 though? what about the 18?

Answer 3

and i will certainly copy your example. thanks!

Answer 4

the 10 makes it a different problem, and not the same one, so you have to figure it out yourself

Answer 5

so a < b+c, b < a+c, and c < a+b is my formula for these problems? and alright :)