5. The area of a hallway is m when measured in square metres, and f when measured
in square feet. The equation that relates m to f is
a. m = 3.3f
b. m = 10.8f
c. f = 3.3m
d. f = 10.8m
The correct answer is option d: f = 10.8m, as 1 square meter equals approximately 10.8 square feet, relating the hallway area measured in square meters (m) to square feet (f).
Conversion Basics
One meter equals 0.3048 feet exactly, so 1 square meter equals (0.3048)^{-2} or about 10.7639 square feet, often rounded to 10.8 in exams. For a hallway area, this means square feet (f) is larger than square meters (m) by this factor. Thus, f ≈ 10.8m holds true.
Option Analysis
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a. m = 3.3f: Incorrect, as 3.3 approximates linear conversion (1m ≈ 3.3ft); squaring gives ~10.8 for area, not linear relation.
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b. m = 10.8f: Wrong direction; this implies square meters exceed square feet, but 1 sq m > 10 sq ft, so m < f.
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c. f = 3.3m: Fails for area; 3.3 suits length (1m to ft), but area requires ~10.8.
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d. f = 10.8m: Correct, matching 1 sq m = 10.8 sq ft (rounded).
| Option | Equation | Why Incorrect/Correct |
|---|---|---|
| a | m = 3.3f | Uses linear factor inversely |
| b | m = 10.8f | Reverses area scale |
| c | f = 3.3m | Linear, not squared |
| d | f = 10.8m | Matches sq m to sq ft |
