A carpenter is cutting common rafters for a roof with a 7:12 pitch. The building width is 7.32 metres. What is the approximate length of the common rafter from the outside of the top plate to the ridge, before accounting for overhangs or ridge board deduction?

Question: A carpenter is cutting common rafters for a roof with a 7:12 pitch. The building width is 7.32 metres. What is the approximate length of the common rafter from the outside of the top plate to the ridge, before accounting for overhangs or ridge board deduction?

Answer options:

• 3.66 metres ✅ 4.20 metres
• 4.88 metres
• 5.05 metres

Correct answer: 4.20 metres

Explanation: The total run of the roof is half the building width, so 7.32 m / 2 = 3.66 m. For a 7:12 pitch, the diagonal factor is calculated as the square root of (7^2 + 12^2) / 12 = square root of (49 + 144) / 12 = square root of (193) / 12 = 13.89 / 12 = 1.1575. The rafter length is then the run multiplied by this factor: 3.66 m * 1.1575 = 4.236 m. Option 4.20 metres is the closest approximation.