One of the corners of the rhombus is three times larger than the other, and its perimeter is 20. Find the area of the rhombus.

univerkov | January 12, 2021 | education

In a rhombus, the lengths of all sides are equal, then AB = BC = СD = AD = Ravsd / 4 = 20/4 = 5 cm.
Let the angle ВAD = X0, then, by condition, the angle ABC = 2 * X0.
A rhombus has the sum of its adjacent angles 1800.
Then the angle ВAD + ABC = X + 2 * X = 1800.
3 * X = 1800.
X = 180/3 = 600.
Angle ВAD = 600.
Determine the area of the rhombus.
Savsd = AВ * AD * Sin60 = 5 * 5 * √3 / 2 = 12.5 * √3 cm2.
Answer: The area of the rhombus is 12.5 * √3 cm2.

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