The two adjacent sides of a rectangle are 5x² − 3y² and x² + 2xy. Find the perimeter.

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Solution

Sides of the rectangle are $l$ and $b$ .
$l = 5 x^{2} - 3 y^{2} b = x^{2} + 2 x y$
Perimeter of the rectangle is $(2 l + 2 b)$ .

$Perimeter = 2 (5 x^{2} - 3 y^{2}) + 2 (x^{2} + 2 x y) = 10 x^{2} - 6 y^{2} + 2 x^{2} + 4 x y 10 x^{2} - 6 y^{2} 2 x^{2} + 4 x y 12 x^{2} - 6 y^{2} + 4 x y Hence, the perimeter of the rectangle is 12 x^{2} - 6 y^{2} + 4 x y .$

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