While in Art class, Alex drew the door to his classroom to be 5 inches. The actual height of this door is 6 ft. 8 inches high. His teacher asked him to use this same scale factor to draw the classroom wall. If the actual height of the wall is 8 ft. how high should Alex draw the wall on his paper?
Answer: 6 inches
Explanation:
This is a proportion problem, however, in order to solve it we must first make sure that the measurements all use the same units. We notice that the problem uses units in inches and in feet. We must convert one into the other. Once the units match then the problem can be solved.
I have chosen to convert the feet into inches taking into consideration that there are 12 inches in one foot:
To convert the actual height of the door: [(6 ft) x (12 inches / 1 ft)] + 8 inches = 80 inches
Notice that the feet units cancel out and we are left with inches.
To convert the actual height of the wall: (8 ft) x (12 inches / 1 ft) = 96 inches
Notice that the feet units cancel out and we are left with inches.
Now we can set up the proportion:
Actual door height / drawn height = Actual wall height / X
80 inches / 5 inches = 96 inches / X
X = [(5 inches) (96 inches)] / 80 inches = 6 inches
Therefore, Alex should draw the wall 6 inches to have it proportional to the other measurements.
©Copyright 2007.Najwa S. Hirn. All rights reserved.
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