To find the correct scale drawing of the playground based on the original rectangle that is 8 units long and 4 units wide (with a scale of 1 box = 5 meters), we first need to determine the dimensions in meters:
- The original dimensions in meters are:
- Length: \( 8 \text{ units} \times 5 \text{ meters/unit} = 40 \text{ meters} \)
- Width: \( 4 \text{ units} \times 5 \text{ meters/unit} = 20 \text{ meters} \)
Next, we want to convert these dimensions into the new scale where 1 box = 20 meters:
- To find out how many boxes are needed:
- New length: \( 40 \text{ meters} \div 20 \text{ meters/box} = 2 \text{ boxes} \)
- New width: \( 20 \text{ meters} \div 20 \text{ meters/box} = 1 \text{ box} \)
Thus, the dimensions of the new rectangle should be 2 units long and 1 unit wide on the new scale.
Now let’s review the given options:
- Rectangle 2 units long and 1 unit wide - matches the dimensions calculated.
- Rectangle 6 units long and 3 units wide - does not match (this would correspond to 120 meters by 60 meters).
- Rectangle 3 units long and 2 units wide - does not match (this would correspond to 60 meters by 40 meters).
- Rectangle 16 units long and 8 units wide - does not match (this would correspond to 320 meters by 160 meters).
Based on this, the correct answer is the rectangle that is 2 units long and 1 unit wide with the scale of 1 box = 20 meters.
1 answer