1. **State the problem:** We have a parallelogram ABCD with sides labeled as follows: - AB = $2a - 12$ - BC = $a - 5$ - CD = $a + 12$ - AD = 19 We need to find the length of each side. 2. **Recall properties of parallelograms:** Opposite sides of a parallelogram are equal in length. Therefore: $$AB = CD \quad \text{and} \quad BC = AD$$ 3. **Set up equations using the property:** $$2a - 12 = a + 12$$ $$a - 5 = 19$$ 4. **Solve the second equation first:** $$a - 5 = 19$$ Add 5 to both sides: $$a - 5 + 5 = 19 + 5$$ $$a = 24$$ 5. **Substitute $a=24$ into the first equation:** $$2(24) - 12 = 24 + 12$$ Calculate each side: $$48 - 12 = 36$$ $$36 = 36$$ This confirms the value of $a$ is correct. 6. **Find the lengths of each side:** - $AB = 2a - 12 = 2(24) - 12 = 48 - 12 = 36$ - $BC = a - 5 = 24 - 5 = 19$ - $CD = a + 12 = 24 + 12 = 36$ - $AD = 19$ (given) **Final answer:** $$AB = 36, \quad BC = 19, \quad CD = 36, \quad AD = 19$$