Geometry (16)

The lengths of the sides of a sandbox are 9ft, 6ft and n ft. Write a compound inequality that describes all possible lengths of n.

A = 9 and b = 6 are the two given sides

The third missing side n can be described through the following inequality

a-b < n < a+b

where a > b ('a' is larger than b)

This is the triangle inequality theorem

So,

a-b < n < a+b

9-6 < n < 9+6

3 < n < 15

Answer: 3 < n < 15

(which means you can pick any number from 3 to 15 for n. You cannot pick 3. You cannot pick 15)