Extend the intersection QR of BA to point M. According to the meaning of the question: AM⊥QR, the quadrilateral ADRM is a rectangle, and the triangle QGH is an equilateral triangle, so QH=HG=AC=2√3, HM=sin angle HAM×HA=2 √3×2√3, MR=AD=AB=4, so QR = 7+2. So PQ.