Hi, there--

THE PROBLEM:
Two sides of a triangle are 9 inches and 17 inches.  What can be the length of the third side?

A SOLUTION:
Use the Triangle Inequality which states that for any triangle, the sum of the lengths of any 
two sides must be greater than the length of the remaining side.

We need to form two inequalities to allow for two cases: Either the 17-inch side of the triangle 
is the longest, or the unknown side is the longest.

Let x be the length of the unknown side.

Then both inequalities must be true.

x + 9 > 17
x > 17 - 9
x > 8

AND

9 + 17 > x
26 > x
x < 26

8 < x < 26
 

The length of x can be any number such that x is greater than 8 and less than 26.

Hope this helps! Feel free to email if you have any questions.

Mrs. Figgy
math.in.the.vortex@gmail.com