1. **Stating the problem:** We have two circles with radii 5 m and 4 m, and the distance between their centers is 6 m. We want to find the length of the line segment where the two circles intersect (the common chord). 2. **Formula and explanation:** When two circles intersect, the length of their common chord can be found using the formula derived from the triangle formed by the centers and the chord: $$d = \text{distance between centers} = 6$$ $$r_1 = 5, \quad r_2 = 4$$ The length of the common chord $c$ is given by: $$c = 2 \sqrt{r_1^2 - \left(\frac{r_1^2 - r_2^2 + d^2}{2d}\right)^2}$$ This formula comes from applying the Pythagorean theorem to the right triangle formed by the radius, half the chord, and the line connecting the centers. 3. **Calculate the term inside the square root:** Calculate the numerator inside the parentheses: $$r_1^2 - r_2^2 + d^2 = 5^2 - 4^2 + 6^2 = 25 - 16 + 36 = 45$$ Divide by $2d$: $$\frac{45}{2 \times 6} = \frac{45}{12} = 3.75$$ 4. **Square this value:** $$3.75^2 = 14.0625$$ 5. **Calculate $r_1^2$:** $$5^2 = 25$$ 6. **Subtract to find the value under the square root:** $$25 - 14.0625 = 10.9375$$ 7. **Find the square root:** $$\sqrt{10.9375} \approx 3.307$$ 8. **Calculate the length of the chord:** $$c = 2 \times 3.307 = 6.614$$ **Final answer:** The length of the common chord where the two circles intersect is approximately **6.61 meters**. This method uses a single formula merging all steps, suitable for Primary 6 level understanding by breaking down each part clearly.