Final answer:
The area of the backyard is calculated by multiplying the length and breadth of the rectangle. After expanding the expression and combining like terms, considering 'c' must be zero, the area is found to be 9a² - 4b², which corresponds to option A.
Step-by-step explanation:
To find the area of the backyard, which is shaped as a rectangle, we need to multiply its length by its breadth. The length of the rectangle is given as 3a+2b meters and the breadth is given as 3a-2b+c meters. To calculate the area, we use the following formula:
Area = Length × Breadth
Substitute the given dimensions into the formula:
Area = (3a+2b) × (3a-2b+c)
Expanding this expression:
Area = 9a² - 4b² + 3ac - 2bc + 2ac - 2b² + c²
Combine like terms:
Area = 9a² - 4b² + 5ac - 2bc + c²
As the question does not contain terms with ac, bc, or c², we can infer that 'c' must equal zero, and thus, the correct answer is:
Area = 9a² - 4b² (Option A)