Chapter 6.4, Problem 1WE

To determine

The numbers that best complete the statements.

Answer to Problem 1WE

The length of third side must greater than 3 but less than 15.

Explanation of Solution

Given information :

The given sides of a triangle are 6 and 9.

The sides of triangle are 6 and 9

Let $x$ be the length of the third side.

A triangle is possible only when the sum of two sides must be greater than the third sides.

So,

  $x+6>9\Rightarrow x>3$ and $6+9>x\Rightarrow x<15$

Therefore, the length of third side must greater than 3 but less than 15.