Slope, m, is equal to the ratio between the change in y and the change in x
m ≤ 3/4 (green line in the attached illustration)
Δx = 0.83 ft
Δy represents the height of each step (red lines in the attached illustration)
The height of each step should be 0.6225 ft
Since the whole staircase measures 9 ft high,
9 ÷ 0.6225 = 14.45
There should be 14.45* steps
in the staircase.
*This seems illogical because how can you have a 0.45 step, right?
Since the problems says that the slope CANNOT exceed 3/4 (it did not say that the slope is EQUAL to 3/4), we may change the slope of the line such that we will get an integer for the number of steps.
I worked backwards and found out that using m=60/83
(which is less than 3/4, and thus satisfies the given condition) will give a better result:The height of each step will be 0.6 ft.
9 ÷0.6 = 15So, there will be a total of 15 steps in the staircase.