The parallelogram heights are 4 cm and 6 cm, and one of its sides is 4 cm larger than the other. Find the perimeter.

univerkov | February 22, 2021 | education

Let side AB = BC = X cm, then, by condition, side AD = BC = (X + 4) cm.

Determine the area using the side of the СD and the height of the ВVC.

S = DC * ВK = X * 6 cm2.

Determine the area using the height of the HВ and the required base AD.

S = AD * BH = (X + 4) * 4 cm2.

Since the areas are the same, let’s equate their right-hand sides.

X * 6 = (X + 4) * 4.

X * 6 = X * 4 + 16.

X * 2 = 16.

X = AB = CD = 8 cm.

BC = AD = 8 + 4 = 12 cm.

Determine the perimeter of the parallelogram.

P = 2 * (AB + AD) = 2 * (8 + 12) = 40 cm.

Answer: The perimeter is 40 cm.

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