Chapter 11, Problem 18CUR

To determine

To Find: Possible Values for the third side of the triangle.

Answer to Problem 18CUR

Possible values for third side $x$ can be 4, 5, 6, 7, 8, 9, and 10.

Explanation of Solution

Given:

Sides of a triangle are 4, 7 and $x$ , $x$ is an integer.

If two sides of a triangle are $a$ and $b$ ( $a>b$ ) then the third side

  $c$ lies in the following interval:

  $a-b<c<a+b$

Applying the above property:

  $\begin{array}{l}7-4<x<7+4\\ \Rightarrow 3<x<11\end{array}$

Possible values for third side $x$ can be 4, 5, 6, 7, 8, 9, and 10.