An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 45 cm, find the sum of the perimeters of all the triangles.
Choose the correct answer:
A) 180 cm  B) 220 cm  C) 240 cm  D) 270 cm  E) 300 cm

Rationale: "we have 45 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 22.5 and continues . so we have 45 , 22.5 , 11.25 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 45 / 1 - ( 1 / 2 ) = 90 equilateral triangle perimeter is 3 a = 3 * 90 = 270 . so option d ."
Answer: D