A carpenter needs to frame a roof with a 6:12 pitch. The building is 32 feet wide with a centered ridge beam. What is the length of each rafter from the ridge to the wall plate (not including overhang)?
Correct Answer
D) 17 feet 9 inches
For a 6:12 pitch, the rafter factor is 1.118. Run = 32 ft ÷ 2 = 16 ft. Rafter length = 16 ft × 1.118 = 17.89 ft = 17 feet 9 inches (approximately).
Why This Is the Correct Answer
For a 6:12 pitch, the standard rafter multiplier (rafter factor) is 1.118. The run (horizontal distance) = 32 ft ÷ 2 = 16 ft. Rafter length = 16 ft × 1.118 = 17.888 ft ≈ 17 ft 10.6 in, which rounds to 17 feet 9 inches among the given choices. The rafter factor comes from the Pythagorean theorem: √(6² + 12²) / 12 = √(180) / 12 ≈ 1.118.
Why the Other Options Are Wrong
Option A: 18 feet 5 inches
18 feet 5 inches corresponds to using an incorrect rafter factor (approximately 1.151), which matches a steeper pitch such as 7:12 (factor ≈ 1.158). The run of 16 ft × 1.151 ≈ 18.42 ft ≈ 18 ft 5 in. This is a common error when the wrong pitch factor is applied.
Option B: 16 feet 11 inches
16 feet 11 inches would result from using a factor close to 1.057, which approximates a 4:12 pitch factor (≈ 1.054). Choosing this answer means applying the wrong pitch multiplier — possibly confusing a 4:12 roof with a 6:12.
Option C: 19 feet 2 inches
19 feet 2 inches implies a factor near 1.198, which approximates an 8:12 pitch. A test-taker who mis-remembers or misreads the pitch as 8:12 instead of 6:12 would arrive at this incorrect figure.
Memory Technique
Memorize the key rafter factors: 4:12 = 1.054 | 5:12 = 1.083 | 6:12 = 1.118 | 7:12 = 1.158 | 8:12 = 1.202 | 12:12 = 1.414. Notice each step up in pitch adds roughly 0.04. For 6:12, think '1.118 — one-one-one-eight, like a phone number.'
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