If one side of an equilateral triangle is 12 cm . The mid points of its sides are joined to form another triangle whose mid points are in turn joined to form still another triangle, this process continues indefinitely then the ratio of sum of areas to sum of altitudes is

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4:1

2:3

3:2

1:4

answer is A.

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Detailed Solution

$(Δ_{1} + Δ_{2} + Δ_{3} + .........) : (h_{1} + h_{2} + h_{3} + .......)$

$= \frac{\sqrt{3}}{4} [{(12)}^{2} + {(6)}^{2} + {(3)}^{2} + .....] : \frac{\sqrt{3}}{2} [(12) + (6) + (3) + ........] = 4 : 1$

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