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 60 cm, find the sum of the perimeters of all the triangles.
Pick one:	A) 180 cm	B) 220 cm	C) 240 cm	D) 270 cm	E) 360 cm
We have 60 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 30 and continues.   So we have 60,30,15,...   We have ratio = 1/2, and it is GP type.   Sum of infinite triangle is a/1-r = 60/1-(1/2) = 120   Equilateral triangle perimeter is 3a = 3*120= 
<gadget id="calculator">3*120</gadget>
<output>360</output>
360.   So option 360 cm.
<result>E</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 60 cm, find the sum of the perimeters of all the triangles.