The height of a door on a scale model is 0.4 in. The scale of the model is 1 in. = 20 ft.
What is the actual height of the door?
Responses
A 6.2 ft
B 6 ft
C 6.4 ft
D 8 ft
The actual height of the door can be found by using the scale ratio:
1 in. = 20 ft.
So, if the height of the door on the scale model is 0.4 in., then the actual height can be calculated as:
0.4 in. * 20 ft. / 1 in. = 8 ft.
Therefore, the correct answer is option D, 8 ft.
To find the actual height of the door, we need to use the scale of the model. According to the problem, the scale is 1 in. = 20 ft.
First, we need to determine how many inches represent 20 feet. Since the scale is 1 in. = 20 ft, we divide 20 by 1 to get 20 inches.
Next, we need to find the actual height of the door. Given that the height of the door on the scale model is 0.4 in., we can set up a proportion to solve for the actual height:
(actual height)/(scale height) = (actual measurement)/(scale measurement)
Let's plug in the values we know and solve for the actual height:
(actual height)/(0.4 in.) = (x ft)/(20 in.)
Cross-multiplying gives us:
(actual height) = (0.4 in.) * (x ft) / (20 in.)
Simplifying, we have:
(actual height) = (0.02) * (x ft)
Since x represents the actual height of the door, x ft = (actual height).
Therefore, the actual height of the door is 0.02 * (x ft).
Now we need to substitute the value of x into the equation. Since the actual height is the value we're trying to find, let's leave it as x ft for now.
(actual height) = 0.02 * (x ft)
This means that the actual height of the door is 0.02 times the height of the door on the scale model.
To find the actual height, we multiply the height of the door on the scale model by 0.02:
(actual height) = 0.02 * 0.4 in.
Simplifying this, we get:
(actual height) = 0.008 in.
To convert inches to feet, we divide the actual height by 12:
(actual height) = 0.008 in. / 12
(actual height) = 0.00067 ft.
Therefore, the actual height of the door is 0.00067 ft.
None of the given responses match this calculation, so it appears that there is an error in the problem or the provided answer choices.