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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

Respuesta :

The tread depth of the stairway is 10.6 according to the riser tread formula.

According to the statement

we have to find the tread depth of the stairway.

So, For this purpose, we know that the

The riser tread formula is the typical interior stair dimension is calculated as the formula, riser (R)+ tread (T) = 17 inches minimum, or 18 inches maximum, not including the nosing. The nosing is the projecting edge of a tread.

Here, The given information is:

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.

So, The tread depth of the stairway is 10.6 according to the riser tread formula.

Learn more about riser tread formula here

https://brainly.com/question/27172305

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