Q. 175.0( 3 Votes )

# The two adjacent sides of a rectangle are 2x^{2} – 5xy + 3z^{2} and 4xy – x^{2} – z.

Answer :

Two adjacent sides are 2x^{2} – 5xy + 3z^{2} and 4xy – x^{2} – z.

Area of rectangle = (2x^{2} – 5xy + 3z^{2})× (4xy – x^{2} – z)

⇒ Area of rectangle = 2x^{2}(4xy – x^{2} – z)-5xy(4xy – x^{2} – z) + 3z^{2}(4xy – x^{2} – z)

⇒ Area of rectangle = 8x^{3}y-2x^{4}-2x^{2}z-20x^{2}y^{2} + 5x^{3}y + 5xyz + 12xyz^{2}-3x^{2}z^{2}-3z^{3}

Perimeter of rectangle = 2× (2x^{2} – 5xy + 3z^{2} + 4xy – x^{2} – z)

⇒ Perimeter of rectangle = 2× (x^{2}-xy + 3z^{2}-z)

⇒ Perimeter of rectangle = (2x^{2}-2xy + 6z^{2}-2z)

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