Subjects geometry

Parallelogram Sides 1F03E1

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Parallelogram Sides 1F03E1


1. **Problem Statement:** We have a parallelogram PQRS with sides PQ = 13 units, QR = (2x - 1) units, and RS = (2x - 3) units. We need to find the measure of side PS. 2. **Important Property:** In a parallelogram, opposite sides are equal in length. Therefore, PQ = RS and QR = PS. 3. **Using the property:** Since PQ = RS, we set: $$13 = 2x - 3$$ 4. **Solve for x:** $$2x - 3 = 13$$ $$2x = 13 + 3$$ $$2x = 16$$ $$x = \frac{16}{2} = 8$$ 5. **Find PS:** Since PS = QR, and QR = (2x - 1), substitute $x=8$: $$PS = 2(8) - 1 = 16 - 1 = 15$$ 6. **Final answer:** The measure of side PS is **15 units**.