Which of the following sets of numbers could represent the three sides of a triangle? Answer \( \begin{array}{ll}\{6,20,26\} & \{15,17,32\} \\ \{13,24,35\} & \{5,18,25\}\end{array} \)

To check if a set of numbers can represent the sides of a triangle, you can use the triangle inequality theorem. This states that for any triangle with sides \(a\), \(b\), and \(c\), the following must be true: 1. \(a + b > c\) 2. \(a + c > b\) 3. \(b + c > a\) Using this theorem, you can evaluate the given sets. After applying these rules, you'll find that \(\{6, 20, 26\}\) does satisfy the triangle inequality (6 + 20 > 26 is false, so it's not a triangle). However, \(\{15, 17, 32\}\) does not (15 + 17 is not greater than 32), while \(\{13, 24, 35\}\) and \(\{5, 18, 25\}\) do represent valid triangles. Exploring the fascinating world of triangles, did you know they are the simplest polygon, possessing only three sides and three angles? This simplicity doesn’t just help in construction and architecture, but also in fields like art and computer graphics, proving that sometimes the simplest shapes can create the most complex designs! Triangles have this unique relationship with math known as the Pythagorean theorem, which only applies to right triangles. It can unlock many mysteries in real life! For instance, if you're trying to build a ramp or a roof, understanding how to calculate the lengths of the sides will ensure it's structurally sound and visually appealing! So grab those tools and enjoy crafting!