Final answer:
The correct dimensions for the rectangle with a perimeter of 20 inches is 5 inches by 5 inches (Option D). The square with a perimeter of 20 inches also has dimensions of 5 inches by 5 inches (Option A) since all sides are equal.
Step-by-step explanation:
Selecting Dimensions for Rectangles and Squares
To find the dimensions of a rectangle with a perimeter of 20 inches, we apply the formula for the perimeter of a rectangle, which is P = 2l + 2w where P is the perimeter, l is the length, and w is the width. The dimensions that make up a perimeter of 20 inches could be in various combinations, but they need to satisfy the equation. For a square with a perimeter of 20 inches, since all sides of a square are equal, we use the formula P = 4s, where s is the side length. Therefore, each side of the square is 5 inches.
To answer the student's questions:
- The dimensions of the rectangle could be 5 inches by 5 inches (Option D), since 5 + 5 + 5 + 5 = 20 inches.
- The dimensions of the square are 5 inches by 5 inches (Option A), as calculated above.
It's important to note that none of the other options for the rectangle satisfy the perimeter requirement. For example, Option A, 20 inches by 1 inch, would result in a perimeter of 42 inches (not 20 inches). Similar logic eliminates Options B and C.