1. **Problem statement:** In the parallelogram ABCD, given BC = 20 cm, BL = 10 cm, and DM = 18 cm, calculate the perimeter of ABCD. 2. **Recall properties of parallelograms:** Opposite sides are equal in length. So, AB = DC and BC = AD. 3. **Given:** BC = 20 cm, BL = 10 cm, DM = 18 cm. 4. Since BL and DM are perpendicular segments from points B and D respectively, and given the lengths, we can infer the sides: - BC = 20 cm (given) - AD = BC = 20 cm (opposite sides equal) 5. To find AB and DC, note that BL and DM are heights from B and D to sides AD and AB respectively. 6. Using the Pythagorean theorem in triangles formed by these heights: - AB = \sqrt{BL^2 + DM^2} = \sqrt{10^2 + 18^2} = \sqrt{100 + 324} = \sqrt{424} = 2\sqrt{106} \approx 20.59 \text{ cm} 7. Since AB = DC, both are approximately 20.59 cm. 8. **Perimeter formula:** $$\text{Perimeter} = 2(AB + BC)$$ 9. Substitute values: $$= 2(20.59 + 20) = 2(40.59) = 81.18 \text{ cm}$$ **Final answer:** The perimeter of parallelogram ABCD is approximately 81.18 cm.