The angle between the diagonals of the rectangle is 120 degrees and the smaller side is 5 cm

The angle between the diagonals of the rectangle is 120 degrees and the smaller side is 5 cm, find the sum of the diagonals of the triangle.

Let the rectangle ABCD be given, and the point of intersection of the diagonals AC and BD, point O. The smaller side AB = CD = 5 cm.

Greater angle <AOD = 120 ° Sum (AC + BD) =?

Since the angle <AOD = 120 °, the angle <COD = (180 ° – 120 °) = 60 °.

And as a consequence, the triangle OCD is equilateral, since, first of all, the triangle is isosceles (CO = OD), and the angle at the vertex O is 60 °. In an equilateral triangle, all sides, like all angles, are equal. So, half of the diagonals OC = OD = CD = 5 (cm).

The sum of the diagonals (AC + BD) = 2 * (OC + OD) = 2 * (5 + 5) = 20 (cm).