How many pieces of 16′ lumber are needed for the soleplates and double top plates of a building 40′ wide and 30′ long?
a. 18
b. 27
c. 22
d. 33
The correct answer and explanation is:
To determine how many pieces of 16′ lumber are needed for the soleplates and double top plates of a building that is 40′ wide and 30′ long, let’s break it down.
Soleplates:
The soleplate runs along the perimeter of the building. In this case, the building has two dimensions, 40′ and 30′.
The perimeter of the building is calculated as:
- 2 * (40′ + 30′) = 140′ (This accounts for both sides of the width and length of the building.)
Double Top Plates:
For double top plates, you will need to add an additional 2 pieces of lumber (one for each layer) along the same perimeter.
The total length of lumber needed for both the soleplates and the double top plates is:
- Soleplates: 140′
- Double Top Plates: 2 * 140′ = 280′
The total length of lumber needed is:
- 140′ (soleplates) + 280′ (double top plates) = 420′
Calculating the Number of 16′ Pieces:
Since each piece of lumber is 16′ long, the total number of 16′ pieces required is:
- 420′ ÷ 16′ = 26.25, which rounds up to 27 pieces.
Therefore, the correct answer is:
b. 27
This ensures that there is enough lumber to cover the entire length for both the soleplates and the double top plates, even if there is a slight excess.