Final answer:
None of the provided options A, B, C, or D serve as valid counterexamples to the original statement that a rectangle with a perimeter of 24 has a length of 8 and a width of 4. The original statement implies fixed dimensions, yet there could be other combinations of length and width yielding the same perimeter, none of which are represented by the options.
Step-by-step explanation:
If the perimeter of a rectangle is 24, then the length is 8 and the width is 4. A counterexample would show that these dimensions are not the only possibility for achieving a perimeter of 24. One example would be:
This still gives us a perimeter of 24 because 2(Length) + 2(Width) = 2(6) + 2(6) = 12 + 12 = 24.
Now, let's look at the provided options:
- The perimeter of a rectangle is 20, and the length is 7. - This does not provide a counterexample to the original statement as the perimeter is different.
- The perimeter of a rectangle is 26, and the length is 6. - Again, this does not provide a counterexample because the perimeter is not 24.
- The perimeter of a rectangle is 24, and the length is 10. - This could be considered a counterexample if the width would adjust to maintain the perimeter of 24, but in this case, it would lead to a negative width, which is not possible.
- The perimeter of a rectangle is 28, and the length is 12. - The perimeter here is different, so it is not a counterexample.
Therefore, none of the provided options A, B, C, or D serve as valid counterexamples to the original statement that a rectangle with a perimeter of 24 would have a length of 8 and a width of 4.