Chapter 6.4, Problem 6WE

To determine

To calculate: between which two numbers length of third side lies

Answer to Problem 6WE

  $5<\text{third}\text{side}<2k+5$

Explanation of Solution

Given information: The lengths of two sides of a triangle are $k,k+5$

Formula used: The length of each side is greater than the difference between the remaining two sides and less than the sum of the lengths of the other two sides.

Calculation:

The lengths of two sides of a triangle are $k,k+5$

Difference between the remaining two sides $k+5-k=5$

Sum of the lengths of the other two sides $=k+5+k=2k+5$

As the length of each side is greater than the difference between the remaining two sides and less than the sum of the lengths of the other two sides,

  $5<\text{third}\text{side}<2k+5$