Final answer:
The green square should be 5 inches wide in each direction to accommodate a 1/4 inch border around the 4 1/2 inch blue square.
Step-by-step explanation:
To determine the size of the green square that will back a blue square with a 1/4 inch border, you need to add twice the width of the border to each dimension of the blue square. Since the blue square is 4 1/2 inches in each direction, you add 1/4 inch twice (once for each side of the square), which equals 1/2 inch.
- Dimension of blue square: 4 1/2 inches
- Width of one green border: 1/4 inch
- Total additional border width: 1/4 inch + 1/4 inch = 1/2 inch
Now you calculate the dimensions of the green square:
- Add the additional border width to the blue square's dimensions: 4 1/2 inches + 1/2 inch = 5 inches.
- So, the green square needs to be 5 inches wide on each side to allow for the 1/4 inch border around the blue square.