Question

kai is building a triangular planting bed. two of the sides have lengths of eight feet and five feet. what are the possible lengths for the third side? 2 - 11 hw etool/ homework help

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the sides of the triangle be \(a = 8\) feet, \(b = 5\) feet, and \(c\) be the third - side. Then \(a + b>c\), \(a + c>b\), and \(b + c>a\).
From \(a + b>c\), we have \(8 + 5>c\), so \(c<13\).
From \(|a - b|

Answer:

The possible lengths of the third side \(c\) satisfy the inequality \(3 < c<13\) (in feet).