Rectangle ABCD has a length represented by the expression 2x-3, and a width represented by the expression 4x+5. Rectangle PQRS has a length represented by the expression x-1, and a width represented by the expression 3x+2. Which Expression can be used to represent the difference in the perimeter of Rectangle ABCD and Rectangle PQRS

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Complete Question

Rectangle ABCD has a length represented by the expression 2x – 3, and a width represented by the expression 4x + 5. Rectangle PQRS has a length represented by the expression x – 1, and a width represented by the expression 3x + 2. Which Expression can be used to represent the difference in the perimeter of Rectangle ABCD and Rectangle PQRS?

a) 2x + 1

b) 4x + 2

c) 4x + 6

d) 20x + 6

b) 4x + 2

Step-by-step explanation:

The Formula for the Perimeter of a Rectangle = 2(L + W)

= 2L + 2W

Hence:

For rectangle ABCD

Length = 2x - 3

Width = 4x + 5

Hence, the Perimeter is :

P = 2L + 2W

P = 2(2x - 3) + 2(4x + 5)

P = 4x - 6 + 8x + 10

P = 4x + 8x -6 + 10

P = 12x + 4

For Rectangle PQRS

Length = x - 1

Width = 3x + 2

Hence, the Perimeter is :

P = 2L + 2W

P = 2(x - 1) + 2(3x + 2)

P = 2x - 2 + 6x + 4

P = 2x + 6x - 2 + 4

P = 8x + 2

The Expression that can be used to represent the difference in the perimeter of Rectangle ABCD and Rectangle PQRS is

Perimeter of Rectangle ABCD - Perimeter of Rectangle PQRS

(12x + 4) - (8x + 2)

12x + 4 - 8x - 2

12x - 8x +4 -2

4x + 2

Option b) 4x + 2 is the correct option.

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