Question

An architect wants to use the riser-tread formula to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. With the architect’s constraints, which of the following must be the tread depth, in inches, of the stairway? (1 foot = 12 inches)

A) 7.2
B) 9.5
C) 10.6
D) 15

Answer 1

Option C

The answer is 10.6

Step-by-step explanation:

Here,

Total rise = 9 feet

Now, 1 foot = 12 inch

So, 9 x 12 inches = 108 inches

A riser height between 7 and 8 inches,

i.e., 8 ≤ h ≤ 7

Total riser = xh ...(1)

where x is the number of steps and h is the riser's height.

From equation (1),

x = Total riser ÷ h

Total riser = 108

h = 8 ≤ h ≤ 7

Thus,

x = 108/8 ≤ h ≤ 108/7

x = 14 ≤ h ≤ 15 ....(2)

Since the number of steps (x) is an odd number,

So, x = 15 [from equation (2)] (.°. 14 is not an odd number)

Also, from equation (1),

h = total riser/x

h = 108/x = 108/15 = 7.2 [it's between 7 and 8]

from riser-tread formula,

2h + d = 25

d = 25 - 2h

d = 25 - 2(7.2)

d = 25 - 14.4

d = 10.6

Thus, The answer is 10.6

-TheUnknownScientist