LUANDATO wrote:In a certain housing development, each garden has the shape of a rectangle whose width is 2/3 its length and the length of the largest garden in the development is 2 times the length of the smallest garden in the development. If the perimeter of the smallest garden is 30 feet, what is the area of the largest garden?
A. 45
B. 54
C. 81
D. 108
E. 216
Each garden has the shape of a rectangle whose width is 2/3 its length.
The perimeter of the smallest garden is 30 feet.
Thus:
W = (2/3)L
2(L + W) = 30, implying that L+W = 15.
Substituting W = (2/3)L into L+W = 15, we get:
L + (2/3)L = 15
3L + 2L = 45
5L = 45
L = 9.
The length of the largest garden is 2 times the length of the smallest garden.
Each garden has the shape of a rectangle whose width is 2/3 its length.
Since the smallest garden has a length of 9, the length of the largest garden = 2*9 = 18.
Thus, the width of the largest garden = (2/3)L = (2/3)(18) = 12.
What is the area of the largest garden?
LW = 18*12 = 216.
The correct answer is
E.
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