Two adjacent sides of a rectangle are
$- 6 x^{2} + 9 y^{2} - 5 x y a n d x^{2} - 2 x + 9 x y$ .
Find its perimeter.

5 x^{2} - 8 x y - 9 y^{2} + 2 x

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10 x^{2} - 8 x y - 18 y^{2} + 4 x

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- 5 x^{2} + 4 x y + 9 y^{2} - 2 x

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- 10 x^{2} + 8 x y + 18 y^{2} - 4 x

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Solution

The correct option is D $- 10 x^{2} + 8 x y + 18 y^{2} - 4 x$
Given: Sides of a rectangle are $- 6 x^{2} + 9 y^{2} - 5 x y a n d x^{2} - 2 x + 9 x y$ .
The perimeter of the rectangle = 2(length + breadth)
$P = 2 [(- 6 x^{2} + 9 y^{2} - 5 x y) + (x^{2} - 2 x + 9 x y)]$
Grouping the like terms together,
$P = 2 [(- 6 x^{2} + x^{2}) + 9 y^{2} + (- 5 x y + 9 x y) - 2 x]$
$P = 2 (- 5 x^{2} + 4 x y + 9 y^{2} - 2 x$ )
$P = - 10 x^{2} + 8 x y + 18 y^{2} - 4 x$

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