Question

The measures of two sides of a triangle are 26 inches and 29 inches. If the measure of the third side is x inches, find the range for the value of x.

Answer 1

In a triangle, the sum of any two sides must be greater than the third side. Using this fact, we can set up an inequality to find the range for the value of x:

26 + 29 > x

55 > x

So the third side must be less than 55 inches. Additionally, the third side must be greater than the positive difference between the other two sides, or:

29 - 26 < x

3 < x

Therefore, the range for the value of x is:

3 < x < 55