1. **Problem Statement:** Construct a triangle $\triangle ABC$ such that $AB = 6$ cm, $BC = 4$ cm, and $CA = 5.5$ cm. 2. **Formula and Rules:** To construct a triangle given three sides, use the triangle inequality rule which states that the sum of any two sides must be greater than the third side. Here, check: $$6 + 4 > 5.5, \quad 6 + 5.5 > 4, \quad 4 + 5.5 > 6$$ All are true, so the triangle can be constructed. 3. **Construction Steps:** - Draw a line segment $AB = 6$ cm. - With center $B$, draw an arc with radius $BC = 4$ cm. - With center $A$, draw an arc with radius $CA = 5.5$ cm. - The intersection of these two arcs is point $C$. - Join $AC$ and $BC$ to complete the triangle. 4. **Explanation:** This method uses the property that the point $C$ lies at the intersection of two circles centered at $A$ and $B$ with radii equal to the lengths of sides $CA$ and $BC$ respectively. 5. **Verification:** The constructed triangle satisfies the given side lengths. Final answer: Triangle $\triangle ABC$ with sides $AB=6$ cm, $BC=4$ cm, and $CA=5.5$ cm is constructed using compass and ruler as described.