Final answer:
The total rafter length is calculated by determining the rafter length per segment based on the roof slope and width, adding the overhang, and then multiplying by the number of rafters spaced 16 inches on center. Exact measurements require further calculation or rafter tables.
Step-by-step explanation:
To calculate the total length of the common rafters for the intersecting hip roof, we need to determine the length of rafter per segment and then multiply by the number of rafters based on the 16-inch on-center spacing.
First, we find the total run of the rafters, which does not include the overhang, using the Pythagorean theorem or rafter tables for a slope of 5:12.
Let's assume the rafter length from the edge to the peak for the 30 ft wide structure is L feet (half the width not counting overhang, plus the run for the slope).
Since the rafters are 16 inches on center, there will be a rafter at every 1.33 ft (16 inches converted to feet). To find the total number of rafters, we divide the length of the house (73 ft) by 1.33 ft, which gives us approximately 54.89, which we round up to 55. Therefore, there will be 55 rafters.
Now, the total length of all common rafters is L feet per rafter multiplied by 55 rafters. Without the specific rafter length, we cannot give a numerical answer.
Lastly, we must include the overhang length (2 ft 6 in.) by converting it to feet (2.5 ft) and adding it to the length of each rafter, then multiplying by the total number of rafters.