Question

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?

Answer 1

15

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.