Question

Find the range for the measure of the third side of a triangle given the measures of two sides.

7 and 9

Please explain how you got your answer, thanks!

Answer 1

This is high school geometry

Answer 2

Uhm... are you sure this is high school geometry?

Answer 3

For triangle inequalities?

Answer 4

Summarizing: Imagine you have two sticks in your hand, lengths 7 and 9. Make an angle with them as wide as possible, so they are almost straight. The distance between their opposite ends can get close to, but not reach, 16, and you are still making a triangle.

Now make the angle between them small. You can get the two opposite ends close together, but they will still be a little more than distance 2 apart (9-7=2), while still making a triangle.

So the answer is "between 2 and 16" or, in interval notation, (2,16). Put another way:

2 < length of third side of triangle with sides 7 and 9 < 16