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Answer :
First, we note that [tex]$3\frac{1}{2}$[/tex] feet is equivalent to
[tex]$$3.5 \times 12 = 42 \text{ inches.}$$[/tex]
This means that for a box to fit through the doorway, its width must be less than [tex]$42$[/tex] inches.
Now, let’s check each option:
1. Option A: 36 inches, 42 inches, 40 inches
- [tex]$36 < 42$[/tex] (fits)
- [tex]$42 \not< 42$[/tex] (does not fit)
- [tex]$40 < 42$[/tex] (fits)
Since one box is exactly [tex]$42$[/tex] inches, Option A does not meet the condition.
2. Option B: 42 inches, 43 inches, 38 inches
- [tex]$42 \not< 42$[/tex] (does not fit)
- [tex]$43 > 42$[/tex] (does not fit)
- [tex]$38 < 42$[/tex] (fits)
Two boxes fail to meet the criterion, so Option B is not acceptable.
3. Option C: 40 inches, 37 inches, 41 inches
- [tex]$40 < 42$[/tex] (fits)
- [tex]$37 < 42$[/tex] (fits)
- [tex]$41 < 42$[/tex] (fits)
All three widths are less than [tex]$42$[/tex] inches, which means Option C satisfies the condition.
4. Option D: 38 inches, 40 inches, 42 inches
- [tex]$38 < 42$[/tex] (fits)
- [tex]$40 < 42$[/tex] (fits)
- [tex]$42 \not< 42$[/tex] (does not fit)
One box has a width of [tex]$42$[/tex] inches, so Option D does not work.
Since only Option C has all boxes with widths less than [tex]$42$[/tex] inches, the correct answer is:
[tex]$$\boxed{40 \text{ inches, } 37 \text{ inches, } 41 \text{ inches}}.$$[/tex]
[tex]$$3.5 \times 12 = 42 \text{ inches.}$$[/tex]
This means that for a box to fit through the doorway, its width must be less than [tex]$42$[/tex] inches.
Now, let’s check each option:
1. Option A: 36 inches, 42 inches, 40 inches
- [tex]$36 < 42$[/tex] (fits)
- [tex]$42 \not< 42$[/tex] (does not fit)
- [tex]$40 < 42$[/tex] (fits)
Since one box is exactly [tex]$42$[/tex] inches, Option A does not meet the condition.
2. Option B: 42 inches, 43 inches, 38 inches
- [tex]$42 \not< 42$[/tex] (does not fit)
- [tex]$43 > 42$[/tex] (does not fit)
- [tex]$38 < 42$[/tex] (fits)
Two boxes fail to meet the criterion, so Option B is not acceptable.
3. Option C: 40 inches, 37 inches, 41 inches
- [tex]$40 < 42$[/tex] (fits)
- [tex]$37 < 42$[/tex] (fits)
- [tex]$41 < 42$[/tex] (fits)
All three widths are less than [tex]$42$[/tex] inches, which means Option C satisfies the condition.
4. Option D: 38 inches, 40 inches, 42 inches
- [tex]$38 < 42$[/tex] (fits)
- [tex]$40 < 42$[/tex] (fits)
- [tex]$42 \not< 42$[/tex] (does not fit)
One box has a width of [tex]$42$[/tex] inches, so Option D does not work.
Since only Option C has all boxes with widths less than [tex]$42$[/tex] inches, the correct answer is:
[tex]$$\boxed{40 \text{ inches, } 37 \text{ inches, } 41 \text{ inches}}.$$[/tex]
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