## Geometry: Common Core (15th Edition)

Define the variables: x=width of the garden; y=length of the garden Perimeter of the garden: $2y + 2x$ Since the walkway is 8 ft, it's length and width are extended 8 ft from the original garden. Walkway width (x): $x+16$ Walkway length (y): $y+16$ Formula for perimeter: $2y+2x = P$ Plug in the walkway length and width: (y+16) + (y+16) + (x+16) + (x+16) This combines to $2y + 2x + 64$ When the perimeter of the garden is subtracted, you receive: $2y + 2x + 64 - (2x + 2y) = 64$ Thus, the difference if 64 ft.