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

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Solution

Let length of rectangle = $5 x^{2} - 3 y^{2}$
and breadth = $x^{2} + 2 x y$
$∴$ Perimeter = 2 (Length + Breadth)
$= 2 (5 x^{2} - 3 y^{2} + x^{2} + 2 x y) = 2 (6 x^{2} - 3 y^{2} + 2 x y) = 12 x^{2} - 6 y^{2} + 5 x y$

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