An equilateral triangle is drawn with a side of length a. A new equilateral triangle is formed by joining the midpoints of the sides of the first one. Then a third equilateral triangle is formed by joining the midpoints of the sides of the second; and so on forever. The limit of the sum of the perimeters of all the triangles thus drawn is:
<spanclass=′latex−bold′>(A)</span>Infinite<spanclass=′latex−bold′>(B)</span>541a<spanclass=′latex−bold′>(C)</span>2a<spanclass=′latex−bold′>(D)</span>6a<spanclass=′latex−bold′>(E)</span>421a