# Find the side of the parallelogram if the other side is 5 cm and the diagonal

July 28, 2021 | education

| **Find the side of the parallelogram if the other side is 5 cm and the diagonal is perpendicular to the side and the wound is 4 cm. What is the area of the parallelogram?**

Let the length of the side AD be 5 cm. By condition, the diagonal AC is perpendicular to the side CD, then the triangle ACD is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg CD. CD ^ 2 = AD ^ 2 – AC ^ 2 = 25 – 16 = 9.

CD = 3 cm.

The diagonal AC is the height of the parallelogram drawn to the side of CD, then the area of the parallelogram is equal to: Savsd = CD * AC = 3 * 4 = 12 cm2.

Answer: The length of the second side is 3 cm, the parallelogram area is 12 cm2.

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