What is the total length of 2 x 6 rafter stock needed for a 24' x 42' gable roof with a 4-in-12 slope and 1' overhang?

To determine the total length of 2 x 6 rafter stock needed for a gable roof with specified dimensions, we first need to calculate the rafter length.

The dimensions provided indicate a roof with a span of 42 feet. In a gable roof configuration, each half of the roof will cover half of that span, meaning the run of the roof on each side is 21 feet.

Given the slope of 4-in-12, we can calculate the rise of the roof per horizontal foot. For every 12 horizontal units, the roof rises 4 units. To find the total rise for the 21-foot run, we use the formula:

Total rise = (Run in feet) x (Rise/Run ratio)

Total rise = 21 x (4/12) = 21 x (1/3) = 7 feet

Next, we apply the Pythagorean theorem to find the length of each rafter.

Leg 1 (the run): 21 ft

Leg 2 (the rise): 7 ft

The length of the rafter can be calculated as follows:

Rafter length = √(run² + rise²)

Rafter length = √(21²