Final answer:
The length of the wall, constructed with 400 bricks each measuring 81 inches by 31 inches, is 100 feet when the wall's height is 42 feet.
Step-by-step explanation:
In this problem, we are tasked with calculating the length of the wall using the information that 400 bricks measuring 81 inches by 31 inches are used to build a wall that is 42 feet high. To find the length of the wall, we must convert the measurements of the bricks to feet, calculate the area covered by one brick, and then use the total number of bricks to find the area of the wall. Since the height of the wall is already given, we can divide the total area of the wall by the height to find the length of the wall.
First, we convert the size of one brick to feet:
- 81 inches is equivalent to 81/12 feet
- 31 inches is equivalent to 31/12 feet
The area covered by one brick is then (81/12) feet × (31/12) feet. The total area covered by 400 bricks is 400 × (81/12 feet × 31/12 feet). Once we have the total area, we can divide it by the height of the wall, 42 feet, to get the length of the wall:
Total area / Height = Length of the wall
Calculating these values, we find that the length of the wall is 100 feet.