Maths-
General
Easy
Question
Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches. According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
When designing a stairway, an architect can use the riser-tread formula 
, where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
Hint:
Hint:
- For making inequation, we have to check two things, one is upper limit and other is lower limit.
The correct answer is:
Explanation:
- We have given the least tread depth be 9 inch and the least riser height be 5 inch.
- We have to find the condition for h.
Step 1 of 1:
We just express the riser height in terms of tread height in previous question as
From the equation, we can conclude that when d is least , h will be maximum.
Now,
The least value of riser height or d is 9 inch
So, Max value of h will be
h = 
h = 8
And the least value of h is given 5 inch.
So,
The set of possible value of h will be
So, Option (C)is correct.
In mathematics, inequalities explain the relationship between two non-equal values. When two values are not equal, we frequently use the "not equal symbol ()" to indicate this. However, many inequalities are used to compare the values and determine whether they are less than or greater.
¶A relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols ">"; "<"; "≥"; "≤. "
¶Since the tread depth, 'd' is at least 9 inches, and the riser height, 'h' is at least 5 inches, it follows that h ≥ 5, and d ≥ 9
respectively. Solving for d in the riser tread formula 2h + d = 25 gives d = 25 - 2h. Thus the first inequality, d ≥ 9, is equivalent to
25-2h ≥ 9.
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