The sides of the parallelogram are 3: 5 find the area of the parallelogram if its perimeter is 48

univerkov | August 22, 2021 | education

The sides of the parallelogram are 3: 5 find the area of the parallelogram if its perimeter is 48 and one of the corners is 180.

Let the length of the smaller side of the parallelogram be equal to AB = 3 * X cm, then the length of the larger side is equal to AD = 5 * X cm.

The perimeter of the parallelogram is: Ravd = 2 * (AB + AD) = 2 * (3 * X + 5 * X) = 48.

8 * X = 24.

X = 24/8 = 3.

Then AB = CD = 3 * 3 = 9 cm.

AD = BC = 5 * 3 = 15 cm.

Then Savsd = AB * BC * Sin120 = 9 * 15 * √3 / 2 = 67.5 * √3 cm2.

Answer: The area of the parallelogram is 67.5 * √3 cm2.

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