Triangle ABC is isosceles, with AB=AC and altitude AM=11. Suppose that there is a point D on AM with AD=10 and ∠BDC=3∠BAC. Then the perimeter of △ABC may be written in the form a+b, where a and b are integers. Find a+b.[asy] import graph; size(7cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-1.55,xmax=7.95,ymin=-4.41,ymax=5.3; draw((1,3)--(0,0)); draw((0,0)--(2,0)); draw((2,0)--(1,3)); draw((1,3)--(1,0)); draw((1,0.7)--(0,0)); draw((1,0.7)--(2,0)); label("11",(0.75,1.63),SE*lsf); dot((1,3),ds); label("A",(0.96,3.14),NE*lsf); dot((0,0),ds); label("B",(-0.15,-0.18),NE*lsf); dot((2,0),ds); label("C",(2.06,-0.18),NE*lsf); dot((1,0),ds); label("M",(0.97,-0.27),NE*lsf); dot((1,0.7),ds); label("D",(1.05,0.77),NE*lsf); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); [/asy] geometryperimetertrigonometryquadraticstrig identitiesLaw of Sinesangle bisector