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 30 cm, find the sum of the perimeters of all the triangles.	Pick.
A) 180 cm  B) 220 cm  C) 240 cm  D) 270 cm  E) 300 cm
We have 30 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 15 and continues.   So we have 30,15,7.5,...   We have ratio = 1/2, and it is GP type.   Sum of infinite triangle is a/1-r = 30/1-(1/2) = 60   Equilateral triangle perimeter is 3a = 3*60= 
<gadget id="calculator">3*60</gadget>
<output>180</output>
180.   So option 180 cm.
<result>A</result>
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 30 cm, find the sum of the perimeters of all the triangles.