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
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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
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.
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