Chapter 15.2, Problem 22PSC

To determine

To Find: The range of possible values of the length of the third side of triangle.

Answer to Problem 22PSC

  $\begin{array}{l}\text{minimum = }|y-x|\\ \text{ maximum = }|y+x|\end{array}$

Explanation of Solution

Given:

  $\text{Sides of triangle }x\text{ and }y.$

Formula Used:

Sum of two sides should be always greater than the third side.

Calculation:

  $\begin{array}{l}\text{In a triangle the sum of the lengths of any two sides must be greater than the third side}\text{.}\\ \text{⇒}\text{ minimum length of third side = }y-x\\ \text{⇒}\text{ maximum length of third side = }y+x\\ \text{ so the range of third side is }\\ \text{⇒}\text{minimum = }|y-x|\\ \text{⇒}\text{maximum = }|y+x|\end{array}$

Conclusion:

Thus,

  $\begin{array}{l}\text{minimum = }|y-x|\\ \text{ maximum = }|y+x|\end{array}$