$If two adjacent sides of a rectangle measure (2 x^{2} + y) m and (x^{2} - y) m, then find its perimeter.$

$6 x^{2} m$

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$- 6 x^{2} m$

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$(6 x^{2} - 4 y) m$

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$(6 x^{2} + 4 y) m$

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Solution

The correct option is A
$6 x^{2} m$

$Perimeter of a rectangle is 2 (l + b), where l = length and b = breadth.$

Let us consider,
$l = 2 x^{2} + y and b = x^{2} - y$

$Perimeter = 2 \times (2 x^{2} + y)$ + $2 \times (x^{2} - y)$

= ( $4 x^{2} + 2 y$ ) +( $2 x^{2} - 2 y$ )

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

= $6 x^{2} m$

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