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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
Answer:
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.
