Use the image to answer the question.

A grid is shown with a rectangle drawn on it. The rectangle is 10 units long and 6 units wide, labeled with 10 and 6 respectively.

Scale: 1 box = 3 inches

Reproduce the scale drawing of a tabletop so that it has a scale of 1 box = 2 inches. Which shows the new scale drawing?

(1 point)
Responses

1.A grid is shown with a rectangle drawn on it. The rectangle is 5 units long and 3 units wide, labeled with 5 and 3 respectively.

Scale: 1 box = 2 inches

1.Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 5 units long and 3 units wide, labeled with 5 and 3 respectively. Scale: 1 box = 2 inches

2.A grid is shown with a rectangle drawn on it. The rectangle is 15 units long and 6 units wide, labeled with 15 and 6 respectively.

Scale: 1 box = 2 inches

2.Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 15 units long and 6 units wide, labeled with 15 and 6 respectively. Scale: 1 box = 2 inches

3.A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively.

Scale: 1 box = 2 inches

3.Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively. Scale: 1 box = 2 inches

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

1 answer

To solve this problem, we need to adjust the dimensions of the rectangle based on the new scale.

  1. The original dimensions of the rectangle are 10 units long and 6 units wide.
  2. 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.