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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

An architect wants to use the risertread 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 ste class=

Respuesta :

TheUnknownScientist

Answer:

Option C

The answer is 10.6

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

Answer:

Explanation:

The riser-tread formula states riser (R)+ tread (T) = 17 inches minimum, or 18 inches maximum.

Given R is between 7 - 8 inches, T must be between 9 - 11 inches.  So the only choices within this range are B) 9.5 and C) 10.6.

As the number of steps must be odd:

for R between 7 - 8 inches, the total rise of 9 feet i.e. 108 inches requires -

108/7 = 15.4 ~ 16 steps to

108/8 = 13.5 ~ 14 steps

15 steps is an odd number between 14 and 16.

With 15 steps, R = 108/15 = 7.2"

For choice B, R + T = 7.2 + 9.5 = 16.7" which is short of the riser-thread formula.

For choice C, R + T = 7.2 + 10.6 = 17.8" which satisfies the riser-thread formula and is the correct answer.

Edit: I missed the riser-thread formula in this question has been defined as  2h + d = 25. So the above calculation was done with a different definition of the formula but arrived at the same answer.

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