If the sides of a rectangle are 6 xz -4 y -2 xy -3 x -6 units and xy -2 x -4 xz -9 units- then its perimeter isA- 20 xz -2 xy -8 y -10 x -6B- 20 x z-2 x y-8 y-10 x-6- 10 x z-x y-4 y-5 x-3D- 20 x z-x y-4 y-10 x-6

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Addition of Algebraic Expression

If the sides ...

Question

If the sides of a rectangle are $6 x z + 4 y - 2 x y - 3 x + 6$ units and $x y - 2 x + 4 x z - 9$ units, then its perimeter is ___.

20 x z + 2 x y + 8 y + 10 x - 6

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20 x z - 2 x y + 8 y - 10 x - 6

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10 x z - x y + 4 y - 5 x - 3

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20 x z - x y + 4 y - 10 x - 6

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Solution

The correct option is B $20 x z - 2 x y + 8 y - 10 x - 6$
Let the length and the breadth of the rectangle be $6 x z + 4 y - 2 x y - 3 x + 6$ units $x y - 2 x + 4 x z - 9$ units respectively.
Perimeter of the rectangle = 2(length + breadth)
$= 2 [(6 x z + 4 y - 2 x y - 3 x + 6) + (x y - 2 x + 4 x z - 9)]$
Grouping the like terms together, we get
$Perimeter = 2 [(6 x z + 4 x z) + (- 2 x y + x y) + (4 y) + (- 3 x - 2 x) + (6 - 9)]$
$= 2 (10 x z - x y + 4 y - 5 x - 3)$
$= 20 x z - 2 x y + 8 y - 10 x - 6$
Hence, the perimeter of the rectangle is $20 x z - 2 x y + 8 y - 10 x - 6$ units.

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