1995 AIME Problem 9

Triangle ABC is isosceles, with AB=AC and altitude AM=11. Suppose that there is a point D on \overline{AM} with AD=10 and \angle BDC=3\angle BAC. Then the perimeter of \triangle ABC may be written in the form a+\sqrt{b}, where a and b are integers. Find a+b.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.