In the rectangle ABCD, the diagonals intersect at point O. Find the perimeter of the triangle AOB

In the rectangle ABCD, the diagonals intersect at point O. Find the perimeter of the triangle AOB if CAD = 30 degrees, AC = 12cm.

1. The diagonal AC of the rectangle ABCD is the hypotenuse of the right-angled triangle ACD, and the side of the CD rectangle with the leg opposite to the angle of 30 °.

2.CD = AC / 2 = 12/2 = 6 cm.

3. The side of the rectangle is CD = AB = 6 cm.

4. Based on the fact that the diagonals of the rectangle are equal and are halved at the intersection point, we calculate the sides of the triangle AOB:

AO = OС = 12: 2 = 6 cm.

5. We calculate the perimeter of the triangle AOB:

AO + ВO + AB = 6 + 6 + 6 = 18 cm.

Answer: the perimeter of the triangle AOB is 18 cm.