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Brianne is building a staircase between the first and second floors of a house, a height of 9 feet. The tread, or depth of each step must be 10 inches. The slope of the staircase cannot exceed 3/4. How many steps should she plan?

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sqdancefan

Answer:

  15

Step-by-step explanation:

If the depth is 10 inches and the slope is 3/4 or less, then the height is a maximum of ...

  (10 in)(3/4) = 7.5 in

The number of steps in 9 feet must be at least ...

  (9 ft)×(12 in/ft)/(7.5 in/step) = (108/7.5) steps = 14.4 steps

14 steps will make the slope greater than 3/4, so Brianne must plan on at least 15 steps.

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