In a rectangle, the smaller side is 20 cm and forms an angle of 60 degrees with the diagonal.

In a rectangle, the smaller side is 20 cm and forms an angle of 60 degrees with the diagonal. The midpoints of the sides of the rectangle are connected in series. Find the perimeter of the resulting quadrilateral.

1. Let’s define the smaller side of the quadrangle.

20: 2 = 10 cm.

2. We define the large side of the quadrangle, denoting it x cm.

tg 600 = x: 10;

x = 10 * tg 600;

x = 10 * √3;

x = 10 * 1.73;

x = 17.3 cm.

3. Determine the perimeter of the quadrangle.

P = 2 * (10 + 17.3);

P = 2 * 27.3;

P = 54.6 cm.

Answer: The perimeter of the quadrangle is 54.6 cm.