Two adjacent sides of a rectangle are $5 x^{2} - 3 y^{2}$ and $x^{2} - 2 x y$ . Find its perimeter. [3 MARKS]

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Answer: 1 Mark

Given that:
Two adjacent sides of a rectangle are $5 x^{2} - 3 y^{2}$ and $x^{2} - 2 x y$ .

The perimeter of a rectangle is given by:
Perimeter of a rectangle = 2 (Length + Breadth)

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

$= [10 x^{2} - 6 y^{2}) + (2 x^{2} - 4 x y)]$

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

So, the perimeter of the rectangle is $12 x^{2} - 6 y^{2} - 4 x y$ .

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