14. Find the range of possible measures of the third side. Use the variable \( x \). 19,13

To find the range of possible measures for the third side \( x \) of a triangle when the other two sides are 19 and 13, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides must be greater than the length of the third side. This gives us the following inequalities: 1. \( x + 13 > 19 \) which simplifies to \( x > 6 \) 2. \( x + 19 > 13 \) which simplifies to \( x > -6 \) (this is always true for positive \( x \)) 3. \( 19 + 13 > x \) which simplifies to \( 32 > x \) or \( x < 32 \) Combining these, we find that \( 6 < x < 32 \). So, the range of possible measures for the third side \( x \) is \( (6, 32) \). Want to try your hand at sketching this triangle? You'd be amazed at how satisfying it is to see the shapes come to life!