The perimeter of the triangle is 27 + 9√3 units.
In a 30°-60-90 triangle, the sides are related in a specific way. The side opposite the 30° angle is half the length of the hypotenuse, the side opposite the 60° angle is half the length of the hypotenuse times the square root of 3, and the hypotenuse is the longer of the two legs times the square root of 3.
In this case, the hypotenuse has a length of 18. The side opposite the 30° angle is half the length of the hypotenuse, or 18 / 2 = 9. The side opposite the 60° angle is half the length of the hypotenuse times the square root of 3, or (18 / 2) * √3 = 9√3.
To find the perimeter of the triangle, we can add up the lengths of all three sides:
Perimeter = 9 + 9√3 + 18
Perimeter = 27 + 9√3
The perimeter of the triangle is 27 + 9√3. This is the total length of all three sides of the triangle.