In a certain housing development, each garden has the shape

We are given that the length of the largest garden in the development is 2 times the length of the smallest garden in the development. If we let the length of the smallest garden = S, then we can let the length of the largest garden = 2S.

We are also given that the perimeter of the smallest garden is 30 feet. Since the width is 2/3 the length, the width = (2/3)S. Thus, we can create the following equation:

2S + 2(2/3)S = 30

2S +(4/3)S = 30

Multiplying the entire equation by 3 gives us:

6S + 4S = 90

10S = 90

S = 9

Thus, the length of the largest garden is 2 x 9 = 18, and the width of the largest garden is (2/3) x 18 = 12.

Therefore the area of the largest garden is 18 x 12 = 216.

Answer: E