Question 395509: Two sides of a triangle are 7inches and 10inches. Give the range of all possible values for the third side. Found 2 solutions by Jstrasner, richard1234:Answer by Jstrasner(112) (Show Source):
You can put this solution on YOUR website! Hey,
So for this problem we need to look at the two extreme possibilities for this triangle:
First of all, the side that is 10 inches in length is 3 inches longer than the side that is 7 inches, therefore the third side has to be 4 inches or more.
Second of all, if you add the sides together you get 17 inches, therefore the third side has to be 16 inches or less.
Therefore, the range of values is 4 to 16 inches
I hope this helps!
Due to the triangle inequality, the third side must be greater than 3 inches and less than 17 inches. So the entire range of values is . For example, 3.05 or 16.9 could be the third side.
