Question

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Answer 1

Answer:

The answer to your question is:

x = 1

Square's perimeter = 12

Rectangle perimeter = 12

The value of x is one and the perimeter of the square and the rectangle is the same.

Step-by-step explanation:

Data

Side of Square = 4x - 1

Length of rectangle = 2x + 1

Width = x + 2

Perimeters are the same

Process

Square perimeter = 4(4x - 1)

Rectangle's perimeter = 2(2x + 1) + 2(x+ 2)

Then

                 4(4x - 1) =  2(2x + 1) + 2(x+ 2)       Equation

                 16x - 4 = 4x + 2 + 2x + 4      

                 16x - 4 = 6x + 6

                 16x - 6x = 6 + 4

                 10x = 10

                 x = 10 / 10

                 x = 1      

Perimeter of the square = 4(4(1) - 1)

                                        = 4(3)

                                        = 12

Perimeter of the rectangle = 2(2(1) + 1) + 2((1)+ 2)

                                            = 2(3) + 2(3)

                                            = 6 + 6

                                            = 12