Chapter 6.4, Problem 4WE

To determine

The numbers that best complete the statements.

Answer to Problem 4WE

The length of third side must greater than $3n$ but less than $17n$ .

Explanation of Solution

Given information :

The given sides of a triangle are 7n and 10n.

The sides of triangle are 7n and 10n

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,

  $x+7n>10n\Rightarrow x>3n$ and $7n+10n>x\Rightarrow x<17n$

Therefore, the length of third side must greater than $3n$ but less than $17n$ .