SOLUTION: Vitrivius, a Roman architect of the first century BCE, set guidelines in his writings for the relationship between the height (rise) and tread (run) of stairs in a building. He wro

Question 1195435: Vitrivius, a Roman architect of the first century BCE, set guidelines in his writings for the relationship between the height (rise) and tread (run) of stairs in a building. He wrote that the rise should be between 9 and 10 inches, inclusive, per step, and the run should be between 18 and 24 inches, inclusive. Which of the following could NOT be the ratio of rise to run for a set of stairs that follows this guideline?
A) 1/3
B) 5/12
C) 3/8
D) 5/9

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

rise = change in height
run = change in horizontal direction

To get the smallest slope possible, we divide the smallest rise over the largest run.
We divide rise = 9 over run = 24 to get the smallest slope.
Recall that A/B is smallest when we minimize A and maximize B. Both are positive values.

P = smallest slope

In contrast, the largest slope occurs when we go for the largest rise and smallest run
Q = largest slope

Therefore we can say

Convert each slope to decimal form
3/8 = 0.375
5/9 = 0.556 approximately

So,

We can see that choices C and D can be ruled out because they are the endpoints mentioned earlier.

Choice B) 5/12 converts to the approximate decimal form of 0.417 and it is between those endpoints mentioned above. So we can rule out choice B

Choice A) 1/3 = 0.333 approximately is NOT between 3/8 = 0.375 and 5/9 = 0.556
The slope mentioned for choice A is too small, aka too shallow.

Answer: Choice A) 1/3

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