Final answer:
Upon calculating, the area of Spencer's garden with a perimeter of 12 feet and odd-numbered sides appears to be 5 square feet. However, this result doesn't match any of the provided options, indicating a possible error in the question itself.
Step-by-step explanation:
We are tasked with finding the area of Spencer's garden given that it has an odd length and width, and a perimeter of 12 feet. Let's denote the length as 'L' feet and the width as 'W' feet. Since the perimeter (P) of a rectangle is P = 2L + 2W and Spencer's garden has a perimeter of 12 feet, we can express this relationship as:
2L + 2W = 12
Now, simplify by dividing both sides by 2:
L + W = 6
Since both the length and width are odd numbers, their possible values could be 1, 3, or 5, because using any larger odd numbers would exceed the sum of 6. The combination that adds up to 6 is 3 (width) and 3 (length), but since the garden is not a square, this doesn't work. The only other possible combination is 5 (length) and 1 (width). The area (A) of a rectangle is A = L x W, so the area is:
Area = 5 feet x 1 foot = 5 square feet
This option is not listed among the given choices A) 9 square feet, B) 16 square feet, C) 20 square feet, D) 25 square feet. Therefore, there seems to be a mistake in the question, as there is no correct answer provided among the options.