The sides of an equilateral triangle are $(2 a - b)$ cm, $(a + 3 b)$ cm and $(2 a - 2 b + 1)$ cm, then the perimeter of the triangle is:

3

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12

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15

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21

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Solution

The correct option is C $21$ cm
Since length of sides are equal in equilateral triangle therefore,
$2 a - b = a + 3 b$
$⟹ a = 4 b$
Also,
$⟹ 2 a - b = 2 a - 2 b + 1$
$⟹ b = 1$
$⟹ a = 4$
Length of each side $= 2 a - b = 7$ cm
Perimeter $=$ $3$ $\times$ Length
$= 21$ cm

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