To solve this problem, we need to adjust the dimensions of the rectangle based on the new scale.
- The original dimensions of the rectangle are 10 units long and 6 units wide.
- The original scale is 1 box = 3 inches, and we want to convert it to 1 box = 2 inches.
First, we need to convert the dimensions from the original scale:
- Length: 10 units
- Width: 6 units
With the new scale of 1 box = 2 inches, we need to determine how many boxes the original dimensions represent under the new scale.
Since the original scale has 1 box = 3 inches, we convert the dimensions to inches:
- Length in inches: \(10 \text{ units} \times 3 \text{ inches/unit} = 30 \text{ inches}\)
- Width in inches: \(6 \text{ units} \times 3 \text{ inches/unit} = 18 \text{ inches}\)
Now we need to apply the new scale of 1 box = 2 inches:
- Length in boxes: \(30 \text{ inches} \div 2 \text{ inches/box} = 15 \text{ boxes}\)
- Width in boxes: \(18 \text{ inches} \div 2 \text{ inches/box} = 9 \text{ boxes}\)
So, in the new scale, the rectangle should be 15 units long and 9 units wide.
Looking at the provided options, the correct response that reflects these dimensions is:
4. A grid is shown with a rectangle drawn on it. The rectangle is 15 units long and 9 units wide, labeled with 15 and 9 respectively. Scale: 1 box = 2 inches.