Let the single side length of the bigger equilateral triangle be 2 units.
Therefore;
R = ⅓(2√(3)) unit
It implies;
L will be;
(2√(3)/3)² = (⅓(√(3)))² + L² - 2*(⅓(√(3)))*Lcos150
Therefore;
L = -½±½√(5)
L ≠ -½-½√(5)
L = -½+½√(5)
L = ½(√(5)-1) unit
Therefore;
L ÷ R is;
½(√(5)-1) ÷ ⅓(2√(3))
= 3(√(5)-1)/4√(3)
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