Answer:
- 810 linear feet
- 540 board feet
Step-by-step explanation:
You want to know the number of linear feet and board feet required to build the sole and double plates in a construction that has a total wall length of 270'.
Plates
A sole plate is one thickness of 2×4. A double plate is 2 thicknesses. So, the lumber required for the sole and double plates is 1+2 = 3 times the length of the walls:
linear feet = 3 × 270' = 810'
Board feet
A 2×4 has 2/3 board feet per foot of length. Then the number of board feet is 2/3 the number of linear feet:
board feet = (2/3 bd ft/ft)(810 ft) = 540 bd ft
The carpenter needs 810 linear feet of 2×4 stock, which is equal to 540 board feet.
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Additional comment
A sole plate is a 2×4 laid flat, serving as an anchor point for the bottom of the vertical wall studs. A top plate may be single or double, and is found at the top of the wall studs. Usually it will be double if the wall is load-bearing. The length of each such plate is the same as the wall length.
A board foot is nominally 144 cubic inches of lumber. It is the volume of a board that is 1 square foot and 1 inch thick. A 2×4 is nominally 8 square inches in cross section, so one foot of 2×4 is 96 cubic inches or 96/144 = 2/3 of a board foot.
(The actual dimensions of "dimension lumber" are somewhat smaller, as it is planed to uniform size from a rough piece of the nominal dimensions.)
