Rosie is building a wheelchair ramp that is 18 feet long and 2 feet high. She needs to install a vertical support piece 12 feet from the end of the ramp. What is the length of the support piece in inches?

  16 inches (12 ft from low end)

  8 inches (12 ft from high end)

Step-by-step explanation:

From the low end of the ramp, the height is proportional to the length of the ramp. 12 feet is 2/3 of the length of the ramp (12/18 = 2/3), so the height of the ramp at that point is 2/3 of the height of the ramp:

  (2/3)(24 inches) = 16 inches . . . . . . support 12 feet from the low end

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The end of the ramp from which the 12-foot measurement is made is not specified. If the measurement is made from the high end of the ramp, the height difference from 24 inches is proportional to the measurement length. That means a support 2/3 of the distance from the high end will be 16 inches less than 24 inches high, so will be ...

  24 in -16 in = 8 inches . . . . . . support 12 feet from the high end