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What is the theoretical line length of the third gable and stud framed 406 mm (16") on centre from the corner on a roof with 2:3 (8:12) slope?

813 mm

1024 mm

To determine the theoretical line length of the third gable in a roof with a specified slope, it's essential to first understand how the roof slope impacts the measurements. A 2:3 slope or an 8:12 slope indicates that for every 12 horizontal units, the roof rises 8 vertical units, which is a typical measurement in roofing.

To calculate the actual line length, you begin by considering the rise/run ratio of the slope. For a gable end framed at center points 406 mm apart, which represents the vertical spacing of studs at regular intervals, an additional calculation is needed to find the total length considering the angle created by the slope.

Using the Pythagorean theorem, the rise (8) and run (12) can be applied to calculate the slope’s hypotenuse. However, since the question requires the distance from a corner considering these measurements, one must observe that the horizontal distance adds to the overall length of the line needed.

The correct option, which is 1024 mm, comes from the combined total of vertical and horizontal components that make up the effective sloped line, factoring in the spacing between studs along the specified length. Thus, the theoretical line length accurately represents the real construction requirement for framing such

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1465 mm

2097 mm

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