The two adjacent sides of a rectangle are $5 x^{2} - 3 y^{2}$ and $x^{2} + 2 x y$ . Find the perimeter.

12 x^{2} + 5 x y + 9 y^{2}

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12 x^{2} - 6 y^{2} + 4 x y

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7 x^{2} - 3 y^{2} + 4 x y

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8 x^{2} - 8 y^{2} + 3 x y

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Solution

The correct option is C $12 x^{2} - 6 y^{2} + 4 x y$
Given adjacent sides of a rectangle are $5 x^{2} - 3 y^{2}$ and $x^{2} + 2 x y$

we know that the perimeter of a rectangle with adjacent sides $a$ and $b$ is $2 \times (a + b)$

Perimeter $= 2 ((5 x^{2} - 3 y^{2}) + (x^{2} + 2 x y))$

$= 2 (6 x^{2} - 3 y^{2} + 2 x y)$

$= 12 x^{2} - 6 y^{2} + 4 x y$

$∴ P e r i m e t e r = 12 x^{2} - 6 y^{2} + 4 x y$

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