Final answer:
To find the rectangle with the smallest possible perimeter, we need to consider the relationship between the length and width of the rectangle. The answer is A) Length = Width.
Step-by-step explanation:
The question asks us to find the dimensions of a rectangle with the smallest possible perimeter. In order to do this, we need to consider the relationship between the length and width of the rectangle.
A) If the length and width are equal, the rectangle will be a square. This is because a square has all equal sides. The formula for finding the perimeter of a square is P = 4s, where s is the length of one side. Since all sides are equal, the perimeter will be minimized.
B) If the length is twice the width, we can let the width be x. Then the length will be 2x. The formula for finding the perimeter of a rectangle is P = 2l + 2w, where l is the length and w is the width. Plugging in the values, we get P = 2(2x) + 2x = 6x. The perimeter is dependent on x, so it is not minimized.
C) If the length is half the width, we can let the width be x. Then the length will be (1/2)x. The formula for finding the perimeter is the same as in part B, so P = 2(1/2)x + 2x = 3x + 2x = 5x. Again, the perimeter depends on x, so it is not minimized.
D) If the length is not related to the width, there is no fixed relationship between the two measurements. The perimeter could be any value, so it is not minimized.
Therefore, the correct answer is A) Length = Width.