Two adjacent sides of a rectangle are
$3 x^{2} + 4 y^{2} + 4 x y a n d - x^{2} - 2 x - 4 x y .$
The perimeter of the rectangle is .

4 x^{2} + 8 y^{2} - 4 x

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3 x^{2} + 6 y^{2} - 2 x

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x^{2} + 4 y^{2} + 4 x

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2 x^{2} + 4 y^{2} + 2 x

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Solution

The correct option is A $4 x^{2} + 8 y^{2} - 4 x$
Let the length of the rectangle $= (3 x^{2} + 4 y^{2} + 4 x y)$
the breadth of the rectangle $= (- x^{2} - 2 x - 4 x y)$
The perimeter of the rectangle $= 2(length + breadth)$
So, the perimeter
$= 2 [(3 x^{2} + 4 y^{2} + 4 x y) + (- x^{2} - 2 x - 4 x y)]$
Grouping the like terms together, we get
$= 2 [(3 x^{2} - x^{2}) + (4 x y - 4 x y) + (4 y^{2}) - 2 x]$
$= 2 (2 x^{2} + 4 y^{2} - 2 x)$
$= 4 x^{2} + 8 y^{2} - 4 x$

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