Question
Length and Area in Scale Drawings Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration shows a rectangle with a length of 4 meters and a width of 3 meters.
The rectangle shows the outline of a campsite in a national forest. Anna makes a scale drawing of the campsite in which the longer side measures 1 meter. What is the area of the scale drawing in square meters?
(1 point)
Responses
12 square meters
12 square meters
3.5 square centimeters
3.5 square centimeters
0.75 square meters
0.75 square meters
1.33 square meters
Answers
GPT-4o mini
To solve the problem, we need to determine the area of the scale drawing based on the scale given.
1. The original rectangle has a length of 4 meters and a width of 3 meters. Therefore, the area of the original rectangle is:
\[
\text{Area} = \text{Length} \times \text{Width} = 4 \text{ m} \times 3 \text{ m} = 12 \text{ square meters}.
\]
2. In the scale drawing, the longer side (length) is scaled down to 1 meter. To find the scale factor:
\[
\text{Scale factor} = \frac{\text{length of scale drawing}}{\text{length of original}} = \frac{1 \text{ m}}{4 \text{ m}} = \frac{1}{4}.
\]
3. Since the scale reduces both dimensions by the same factor of \(\frac{1}{4}\), the width in the scale drawing will be:
\[
\text{Width of scale drawing} = 3 \text{ m} \times \frac{1}{4} = \frac{3}{4} \text{ m}.
\]
4. Now, we can calculate the area of the scale drawing:
\[
\text{Area of scale drawing} = \text{Length} \times \text{Width} = 1 \text{ m} \times \frac{3}{4} \text{ m} = \frac{3}{4} \text{ square meters} = 0.75 \text{ square meters}.
\]
Thus, the area of the scale drawing is **0.75 square meters**.
**Correct Response: 0.75 square meters**.
1. The original rectangle has a length of 4 meters and a width of 3 meters. Therefore, the area of the original rectangle is:
\[
\text{Area} = \text{Length} \times \text{Width} = 4 \text{ m} \times 3 \text{ m} = 12 \text{ square meters}.
\]
2. In the scale drawing, the longer side (length) is scaled down to 1 meter. To find the scale factor:
\[
\text{Scale factor} = \frac{\text{length of scale drawing}}{\text{length of original}} = \frac{1 \text{ m}}{4 \text{ m}} = \frac{1}{4}.
\]
3. Since the scale reduces both dimensions by the same factor of \(\frac{1}{4}\), the width in the scale drawing will be:
\[
\text{Width of scale drawing} = 3 \text{ m} \times \frac{1}{4} = \frac{3}{4} \text{ m}.
\]
4. Now, we can calculate the area of the scale drawing:
\[
\text{Area of scale drawing} = \text{Length} \times \text{Width} = 1 \text{ m} \times \frac{3}{4} \text{ m} = \frac{3}{4} \text{ square meters} = 0.75 \text{ square meters}.
\]
Thus, the area of the scale drawing is **0.75 square meters**.
**Correct Response: 0.75 square meters**.