GeometryYou have two pieces of wood that will make up two sides of a triangular picture frame. One is 6 in. long and the other is 7 in. long. What is the range of the possible lengths of the frame?

Accepted Solution

x = length of third side
The third side is unknown and can't be determined to be one fixed number. However, we can find a set of values or a range of acceptable values

If we know that 
a = 6
b = 7
are the two given sides, then we can say

b-a < x < b+a
7-6 < x < 7+6
1 < x < 13

So the third side x can be between 1 and 13. 
The third side cannot be equal to 1 unit or 13 units because a triangle would not form. Instead a straight line would form.

Note: This idea is using the triangle inequality theorem