Question

Use Proportional Relationships Unit Test
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Use the image to answer the question.



A grid is shown with a rectangle drawn on it. The rectangle is 8 units long and 4 units wide, labeled with 8 and 4 respectively.
Scale: 1 box = 5 meters

Reproduce the scale drawing of a playground so that it has a scale of 1 box = 20 meters. Which drawing shows the new scale?

(1 point)
Responses



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 = 20 meters

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 = 20 meters



A grid is shown with a rectangle drawn on it. The rectangle is 16 units long and 8 units wide, labeled with 16 and 8 respectively.
Scale: 1 box = 20 meters

Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 16 units long and 8 units wide, labeled with 16 and 8 respectively. Scale: 1 box = 20 meters



A grid is shown with a rectangle drawn on it. The rectangle is 2 units long and 1 unit wide, labeled with 2 and 1 respectively.
Scale: 1 box = 20 meters

Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 2 units long and 1 unit wide, labeled with 2 and 1 respectively. Scale: 1 box = 20 meters



A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively.
Scale: 1 box = 20 meters

Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively. Scale: 1 box = 20 meters
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Answer 1

To find the correct scale drawing of the playground with the new scale of 1 box = 20 meters, we first need to determine the dimensions of the rectangle in meters.

The original rectangle measures 8 units long and 4 units wide, and with the scale of 1 box = 5 meters, we convert the dimensions to meters:
- Length: \( 8 \, \text{units} \times 5 \, \text{meters/unit} = 40 \, \text{meters} \)
- Width: \( 4 \, \text{units} \times 5 \, \text{meters/unit} = 20 \, \text{meters} \)

Now we want to convert these dimensions to a new scale where 1 box = 20 meters:
- To find the new length in units, we divide the length in meters by the new scale:
\( 40 \, \text{meters} \div 20 \, \text{meters/unit} = 2 \, \text{units} \)
- To find the new width in units, we divide the width in meters by the new scale:
\( 20 \, \text{meters} \div 20 \, \text{meters/unit} = 1 \, \text{unit} \)

So, the dimensions of the rectangle in the new scale will be 2 units long and 1 unit wide.

Looking at the provided options:
- The correct choice is the drawing showing a rectangle that is **2 units long and 1 unit wide**, labeled with 2 and 1 respectively.

This matches our calculated dimensions for the new scale, thus that choice shows the correct scale drawing.