In rectangle ABCD, the diagonals intersect at point O, angle CAD = 30 degrees AC = 16 cm.

In rectangle ABCD, the diagonals intersect at point O, angle CAD = 30 degrees AC = 16 cm. Find the perimeter of the triangle COD.

Let us determine the lengths of the sides OD and OS of the triangle COD, knowing by the condition of the problem that the length of the diagonal AC of the rectangle ABCD is 16 centimeters, as well as the fact that the diagonals of the rectangle are equal and are divided by the intersection point in half:

16: 2 = 8.

Determine the length of the CD side of the COD triangle, knowing that the sine of the angle is equal to the ratio of the opposite leg to the hypotenuse:

16 * 1/2 = 8.

Determine the perimeter of the COD triangle:

8 + 8 + 8 = 24.

Answer: The perimeter of the COD triangle is 24 centimeters.