The side of an equilateral triangle are $(3 x + 2 y) c m$ , $(5 x + 6 y) c m$ and $(x + y + 3) c m$ . Then the perimeter of the triangle is :

15 c m

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12 c m

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18 c m

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10.5 c m

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Solution

The correct option is B $12 c m$
Given the sides of equilateral triangle are $(3 x + 2 y), (5 x + 6 y)$ and $(x + y + 3)$
The all sides of equilateral triangle are equal
Then $3 x + 2 y = 5 x + 6 y$
$\Rightarrow 3 x - 5 x = 6 y - 2 y$
$\Rightarrow - 2 x = 4 y$
$\Rightarrow x = - 2 y$ ...................(1)
And $5 x + 6 y = x + y + 3$
$\Rightarrow 5 x - x + 6 y - y = 3$
$\Rightarrow 4 x + 5 y = 3$ ..........(2)
Put the value $x = - 2 y$ as per (1) we get
$4 (- 2 y) + 5 y = 3$
$\Rightarrow - 8 y + 5 y = 3$
$\Rightarrow - 3 y = 3$
$\Rightarrow y = - 1$ ..................(3)
$∴ x = - 2 (- 1) = 2$
Put the value $x = 2$ and $y = - 1$ in length of side
$x + y + 3 = 2 - 1 + 3 = 4$ cm
Then perimeter of triangle $= 3 \times 4 = 12$

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