9. Rachel wants to draw a triangle with sides of length 4 cm and 5 cm . What is a possible length of the third side?

To find a possible length for the third side of a triangle with two sides measuring 4 cm and 5 cm, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, the third side (let's call it \( x \)) must satisfy two inequalities: \( 4 + 5 > x \) and \( x + 4 > 5 \). Solving these gives us \( x < 9 \) and \( x > 1 \). Thus, a possible length for the third side is any value between 1 cm and 9 cm, like 6 cm! The triangle inequality theorem is not only useful in geometry but also has real-world applications, such as in construction and engineering. For instance, when building roof trusses or bridges, ensuring that the lengths of supports (the sides of your triangle) adhere to these principles is crucial for the structure's stability! This ensures that everything holds up against forces like wind, weight, and natural movement.