Hello, igottaquestion!

Tom has two sticks, one 17 inches long and the other 10 inches long.

Joan is looking for another stick so they can build a triangle.

What is the *maximum range* that the length of the third stick can fall within

in order to be able to build a triangle with the three sticks as sides? We have this triangle: Code:

*
* *
* *
10 * * 17
* *
* *
* * * * * * *
x

The Triangle Inequality says:

. . The sum of any two sides must be greater than the third side.

We have: .$\displaystyle x + 10 \:>\:17 \quad\Rightarrow\quad x \:>\:7$

. . . .And: .$\displaystyle 10+17 \:>\:x \quad\Rightarrow\quad 27 \:>\:x \quad\Rightarrow\quad x \:<\:27$

Therefore: .$\displaystyle 7 \:<\:x\:<\:27$