Question
A rectangle measures 10 meters by 6 meters. Clarence makes a scale drawing of the rectangle in which the greater dimension is 2 meters. What is the area of Clarence’s scale drawing?(1 point)
Responses
0.2 square meters
0.2 square meters - no response given
60 square meters
60 square meters - no response given
6.6 square meters
6.6 square meters - incorrect
2.4 square meters
2.4 square meters - no response given
Incorrect
Responses
0.2 square meters
0.2 square meters - no response given
60 square meters
60 square meters - no response given
6.6 square meters
6.6 square meters - incorrect
2.4 square meters
2.4 square meters - no response given
Incorrect
Answers
GPT-4o mini
To find the area of Clarence's scale drawing, we first need to determine the scale factor based on the greater dimension of the original rectangle and the greater dimension of the scale drawing.
The original rectangle measures 10 meters by 6 meters.
1. The greater dimension in the original rectangle is 10 meters.
2. In Clarence's scale drawing, the greater dimension is 2 meters.
To find the scale factor, we can divide the greater dimension of the drawing by the greater dimension of the original rectangle:
\[
\text{Scale factor} = \frac{\text{Greater dimension of the drawing}}{\text{Greater dimension of the original}} = \frac{2 \text{ meters}}{10 \text{ meters}} = \frac{1}{5}
\]
Next, we apply this scale factor to both dimensions of the rectangle:
- The length in the scale drawing:
\[
\text{Length} = 10 \text{ meters} \times \frac{1}{5} = 2 \text{ meters}
\]
- The width in the scale drawing:
\[
\text{Width} = 6 \text{ meters} \times \frac{1}{5} = 1.2 \text{ meters}
\]
Now we can find the area of the scale drawing:
\[
\text{Area} = \text{Length} \times \text{Width} = 2 \text{ meters} \times 1.2 \text{ meters} = 2.4 \text{ square meters}
\]
Thus, the area of Clarence’s scale drawing is **2.4 square meters**.
Since your response indicates that 2.4 square meters is marked as incorrect, it is likely that there was an error or oversight in the exam or source material. However, based on the calculations performed, the area is indeed **2.4 square meters**.
The original rectangle measures 10 meters by 6 meters.
1. The greater dimension in the original rectangle is 10 meters.
2. In Clarence's scale drawing, the greater dimension is 2 meters.
To find the scale factor, we can divide the greater dimension of the drawing by the greater dimension of the original rectangle:
\[
\text{Scale factor} = \frac{\text{Greater dimension of the drawing}}{\text{Greater dimension of the original}} = \frac{2 \text{ meters}}{10 \text{ meters}} = \frac{1}{5}
\]
Next, we apply this scale factor to both dimensions of the rectangle:
- The length in the scale drawing:
\[
\text{Length} = 10 \text{ meters} \times \frac{1}{5} = 2 \text{ meters}
\]
- The width in the scale drawing:
\[
\text{Width} = 6 \text{ meters} \times \frac{1}{5} = 1.2 \text{ meters}
\]
Now we can find the area of the scale drawing:
\[
\text{Area} = \text{Length} \times \text{Width} = 2 \text{ meters} \times 1.2 \text{ meters} = 2.4 \text{ square meters}
\]
Thus, the area of Clarence’s scale drawing is **2.4 square meters**.
Since your response indicates that 2.4 square meters is marked as incorrect, it is likely that there was an error or oversight in the exam or source material. However, based on the calculations performed, the area is indeed **2.4 square meters**.