Chapter 1, Problem 33RP

To determine

To calculate: The upper and lower limits for the length of the side PR

Answer to Problem 33RP

The upper and lower limits of PR are respectively $7<PR<31$

Explanation of Solution

Given information: The values given are $PQ=12$ and $QR=19$

Formula used: Triangular inequality theorem (for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side)

Calculation: Applying triangular inequality in triangle PQR, we get

  

  

Joining the above two equations, we get:

  

  $|12-19|<PR<12+19$