Final answer:
The equation that represents the area of the garden is x^2 - 2x - 4.
Step-by-step explanation:
To find the equation that best represents the area of the garden, we need to multiply the length and width of the garden. The length is given as 2x-4 and the width is 1/2 of the length. So, the width can be represented as (1/2)(2x-4). Now we can write the equation for the area as:
Area = (2x-4) * (1/2)(2x-4)
To simplify the equation, we can distribute and combine like terms:
Area = x^2 - 4x + 2x - 4
Area = x^2 - 2x - 4
Area = (2x-4) \u00d7 (x-2)
To find the simplified form, we multiply the two binomials:
Area = 2x(x-2) - 4(x-2)
Area = 2x^2 - 4x - 4x + 8
Combining like terms, the equation simplifies to:
Area = 2x^2 - 8x + 8