High School

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. Given that 360 feet of antique picket fencing is used to enclose the garden, find the dimensions of the garden.

A) Length: 240 ft, Width: 160 ft
B) Length: 180 ft, Width: 120 ft
C) Length: 120 ft, Width: 80 ft
D) Length: 90 ft, Width: 60 ft

Answer :

Final answer:

The correct option is C) Length: 120ft, Width: 80ft, obtained by solving the given equation.

Explanation:

The question is asking us to find the dimensions of a rectangle that can be enclosed by 360ft of antique picket fencing such that the width is two thirds of the length. In a rectangle, the perimeter is found by the formula 2(length + width). Let's denote the length as L and width as 2L/3, reflecting that the width is two-thirds the length. Thus, the equation that represents the total amount of fencing is 2(L + 2L/3)=360. By solving this equation, we find that L=120ft and the width, which is two-thirds of this, is 80ft. Hence, the correct solution is option C) Length: 120ft, Width: 80ft.

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