The length of a small leg of a 30 degree, - 60 degree, - 90 degree triangle is 3. what is the perimeter of the triangle.

Did you mean "small" or did you mean "shortest?"

Let's assume that the shortest side has length 3. This would be opposite the 30 degree angle. We can form and solve an equation of ratios to solve this problem. Since this is a 30-60-90 degree triangle, the perimeter could be 1x + sqrt (3) x + 2x. 1x is the shortest side, so 1x = 3, and x=3.

Then the perimeter, 1x + sqrt (3) x + 2x, would be 3 + 3sqrt (3) + 6,

or

3 (sqrt (3) + 2).