The diagonal of ABCD paralleogram is BD=2. The angles of triangle BCD are all equal. What is the perimeter of parallelogram?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The parallelogram ABCD has a diagonal BD = 2. The angles of the triangle BCD are equal or they are equal to 60 degrees. As the diagonal intersects the parallelogram into two congruent triangles we have the angle A = angle C = 60 degrees and the angle B = angle D = 120 degrees.

As the triangle BCD has equal angles, so are its sides. This gives BC = CD = BD = 2

The perimeter of the parallelogram is 2 + 2 + 2 + 2 = 8

The perimeter of ABCD is 8 units.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since all the angles of triangle BCD are equal, that means that the triangle BCD is equilateral, therefore BD = BC = CD = 2.

Since ABCD is parallelogram, then BC=AD = 2 and AB = CD = 2.

The perimeter of the parallelogram ABCD is:

P = AB+BC+CD+AD

P = 4*AB

P = 4*2

P = 8 units

The requested perimeter of the parallelogram ABCD is of 8 units.

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