What would be the scale factor if an airplane is 87 feet long; 2 inches = 15 feet
An airplane company wants to make a model of an 87 foot airplane. The scale they are using is 2 in. = 8 ft. How many inches long will the airplane model be?
Set up a proportion, cross multiply and solve for x.
2/15 = x/87
15x = 174
x = 11.6 inches
K12 check it oit 10/100 npt bad
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To determine the scale factor, we need to compare the actual length of the airplane to the length represented on the scale.
Given:
Actual length of the airplane = 87 feet
Scale: 2 inches = 15 feet
First, we need to find the length represented on the scale for 87 feet.
Since 2 inches on the scale represents 15 feet, we can set up a proportion:
2 inches / 15 feet = x inches / 87 feet
To solve for x, we can cross multiply and solve the equation:
2 inches * 87 feet = 15 feet * x inches
174 inches = 15x
Next, divide both sides of the equation by 15 to isolate x:
174 inches / 15 = x
x ≈ 11.6 inches
Therefore, the length of the airplane on the scale is approximately 11.6 inches.
To find the scale factor, we'll compare the length on the scale to the actual length:
Scale factor = Length on scale / Actual length
Scale factor = 11.6 inches / 87 feet
Now, we need to convert the units of the actual length into inches to match the units on the scale:
1 foot = 12 inches
87 feet = 87 * 12 inches = 1044 inches
Scale factor = 11.6 inches / 1044 inches
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
GCD(11.6, 1044) = 0.4 (approximately)
Scale factor = 11.6 inches / 1044 inches
Scale factor = 0.01111 (approximately)
Therefore, the scale factor, when rounding to four decimal places, is approximately 0.0111.