The Aesthetic Garden Problem. A landscape architect wants the length of a rectangular shaped flower garden to be twice the width. The garden should have a total area of 288ft^2. what are the dimensions of the garden?
width = x
length = 2x
(x)(2x) = 288
2x^2 = 288
x^2 = 144
x = √144 = 12
If a person is ordering fencing for a yard which is more important the area or the perimeter.
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To solve this problem, we can use algebraic equations. Let's assume the width of the garden is "w" feet. According to the problem, the length should be twice the width, so the length would be "2w" feet.
The area of a rectangle can be calculated by multiplying its length and width. In this case, we have:
Area = Length × Width
Given that the area is 288ft^2, we can write the equation as follows:
288 = (2w) × w
Now, let's solve this equation for "w" to find the width of the garden:
288 = 2w^2 (Expanding the equation)
w^2 = 144 (Dividing both sides by 2)
w = √(144) (Taking the square root of both sides)
w = 12 ft (Simplifying the square root)
So, the width of the garden is 12 feet. Since the length is twice the width, the length would be:
Length = 2w = 2 × 12 = 24 ft
Therefore, the dimensions of the garden are 24 feet by 12 feet.