The Correct Answer and Explanation is:
Based on the image provided, the question being addressed is number 8.
Correct Answer: The actual length of the window is 6 feet.
Explanation:
This problem is a classic example of using a scale factor to convert a measurement from a model or drawing to its real-world size. The core principle is setting up a proportion that relates the model’s dimensions to the actual building’s dimensions.
The problem provides a specific scale: 1/4 inch on the model represents 2 feet on the actual building. We are also told that a window in the model measures 3/4 of an inch. Our goal is to find the actual length of this window in feet.
One of the most straightforward ways to solve this is by setting up a proportion. A proportion is an equation that states two ratios are equal. We can set up our ratios as (model length) / (actual length).
The first ratio comes from the given scale:
(1/4 inch) / (2 feet)
The second ratio comes from the window measurement, where ‘x’ will represent the unknown actual length:
(3/4 inch) / (x feet)
Now, we set these two ratios equal to each other to form a proportion:
(1/4) / 2 = (3/4) / x
To solve for x, we can cross multiply. This involves multiplying the numerator of the first fraction by the denominator of the second, and setting it equal to the denominator of the first fraction multiplied by the numerator of the second.
(1/4) * x = 2 * (3/4)
First, simplify the right side of the equation:
(1/4) * x = 6/4
Now, to isolate x, you can multiply both sides of the equation by 4. This cancels out the denominators.
x = 6
Therefore, the actual length of the window is 6 feet. This logical process of scaling up from the model’s measurement using the established ratio ensures an accurate conversion.
