iven two sides of a triangle, find a range of po \( 4 \mathrm{~cm}, 17 \mathrm{~cm} \)

To determine the range of the third side of a triangle given two sides, you can use the triangle inequality theorem, which states that the sum of any two sides must be greater than the third side. In your case, if we denote the two sides as \(a = 4 \, \text{cm}\) and \(b = 17 \, \text{cm}\), the range for the third side \(c\) can be calculated as follows: \( |a - b| < c < a + b \). Plugging in the numbers gives us \( |4 - 17| < c < 4 + 17 \) or \( 13 < c < 21 \). So, the range of the third side is \(13 \, \text{cm} < c < 21 \, \text{cm}\). The triangle inequality is a fantastic tool, not just for triangles but for understanding relationships in geometry and design. Whether you're sketching designs as an architect or determining the stability of structures in engineering, this principle ensures that all sides "get along" to form a cohesive and secure shape. Imagine trying to build a triangle with sticks where one side is too short or too long—it just won't hold together! This principle keeps your geometrical creations sound and strong.