Answer:
total area of the garden and walkway = 2a² + 21a + 54
Step-by-step explanation:
The walkway surrounds the rectangular garden. The width of the garden is 9 ft and the length is 12 ft. Since the width of the walkway around the garden is the same on every side let us use a to represent the width around the garden.
The garden is rectangular and the width of the walkway around the garden is uniform. The width added on both end of the width of the rectangle will be 2a while the width added to the both length of the rectangle will be 2a also.
Therefore
total area of the garden and walkway = length × width
length of garden and the walkway = 2a + 12
width of garden and the walkway = 2a + 9
total area of the garden and walkway = (2a + 12)(2a + 9)
total area of the garden and walkway = 4a² + 18a + 24a + 108
total area of the garden and walkway = 4a² + 42a + 108
divide through by 2
total area of the garden and walkway = 2a² + 21a + 54
