The two adjacent sides of a rectangle are 2x² - 5xy + 3z² and 4xy - x² - z². Find its perimeter.

The two adjacent sides of a rectangle = (2x² - 5xy + 3z²) and (4xy - x² - z²)

As we know the perimeter of rectangle = 2 x (l + b)

= 2 $\times$ [(2x² - 5xy + 3z²) + (4xy - x² - z²)]

= 2 $\times$ [2x² - 5xy + 3z² + 4xy - x² - z²]

= 2 $\times$ [(2x² - x²) + (- 5xy + 4xy) + (3z² - z²)]

= 2 $\times$ [x² - 1xy + 2z²]

= 2 $\times$ x² - 2 $\times$ 1xy + 2 $\times$ 2z²

= 2x² - 2xy + 4z²

Hence, the perimeter of rectangle = 2x² - 2xy + 4z²