The actual length (L) of a rectangle is 122 inches. Use the scale drawing of the rectangle to find the actual width (W).
Scale width: 1.8 in. Scale length: 6.1 in.
A. 3.38 in.
B. 36 in.
C. 67.77 in.
D. 219.6 in.
The Correct Answer and Explanation is:
To find the actual width (W) of the rectangle using the scale drawing, we first need to understand the relationship between the scale dimensions and the actual dimensions of the rectangle.
Given:
- Actual length (L) = 122 inches
- Scale length = 6.1 inches
- Scale width = 1.8 inches
The first step is to calculate the scale factor, which is the ratio of the actual length to the scale length. This will help us understand how much larger the actual dimensions are compared to the scale drawing. The scale factor (SF) can be calculated using the following formula:
[
\text{Scale Factor (SF)} = \frac{\text{Actual Length}}{\text{Scale Length}} = \frac{L}{\text{Scale Length}} = \frac{122 \text{ inches}}{6.1 \text{ inches}} \approx 20
]
Next, we can use the scale factor to find the actual width (W). We will first calculate the actual width by applying the same scale factor to the scale width. The formula for finding the actual width using the scale width is:
[
\text{Actual Width (W)} = \text{Scale Width} \times \text{Scale Factor} = 1.8 \text{ inches} \times 20 \approx 36 \text{ inches}
]
Thus, the actual width of the rectangle is approximately 36 inches.
Conclusion:
Therefore, the correct answer is B. 36 inches. This process demonstrates the importance of understanding scale drawings in relation to actual measurements. By calculating the scale factor from the given length and applying it to the width, we can accurately determine the actual dimensions of objects represented in scaled formats. This skill is especially valuable in fields such as architecture, engineering, and design, where precise measurements are crucial for creating functional and aesthetically pleasing structures and products.