Chapter 15.3, Problem 19PSB

To determine

To Find: The total possible number triangles that can be formed having all sides integers.

Answer to Problem 19PSB

  $100<x<1500$

Explanation of Solution

Given:

  $\to \text{Two sides of triangle }700\text{ and 800 }$

Formula Used:

The sum of length of two sides of any triangle is always greater than the third side.

So, Maximum triangle that could be formed

  $\text{⇒}\text{Greater side}-\text{smaller side}<x<\text{Greater side}+\text{smaller side}$

Calculation:

  $\begin{array}{l}\text{⇒}\text{Greater side}-\text{smaller side}<x<\text{Greater side}+\text{smaller side}\\ \text{⇒}800-700<x<800+700\\ \text{⇒}100<x<1500\end{array}$

Conclusion:

Thus total possible triangle exits are $100<x<1500$