The perimeter of the rhombus is 16 cm, the height drawn from the top of the obtuse angle divides the side

| September 6, 2021 | education

The perimeter of the rhombus is 16 cm, the height drawn from the top of the obtuse angle divides the side of the rhombus in half. Find the corners of the rhombus and the side?

In a rhombus, all four sides are equal, opposite angles are equal, opposite sides are parallel. The sum of all the angles of the rhombus is 360 °. The perimeter of a rhombus is four times the length of one of its sides.

1. Determine the length of one side of the rhombus.

16/4 = 4 cm.

Consider a triangle formed by a height, a side of a rhombus equal to 4 cm and half of the other side equal to 2 cm. The triangle is rectangular. The hypotenuse is 4 cm, the leg is 2 cm, that is, it lies opposite an angle of 30 °. This means that the acute angle of the rhombus is 60 °.

2. Find the value of the obtuse angle of the rhombus.

(360 – 60 * 2) / 2 = 120 °.

Answer: The side of the rhombus is 4 cm. The angles of the rhombus are: 60 °, 60 °, 120 °, 120 °.



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