Let's break the problem down into parts and solve each step-by-step:
1. Find the length and breadth of the rectangular field.
The length of the rectangular floor is given as 12 meters, and the breadth is given as 8 meters.
2. Find the area of the rectangular floor.
- The area of a rectangle is calculated using the formula:
[tex]\[
\text{Area} = \text{Length} \times \text{Breadth}
\][/tex]
- Substituting the given values:
[tex]\[
\text{Area} = 12 \, \text{meters} \times 8 \, \text{meters} = 96 \, \text{square meters}
\][/tex]
3. If the length and width of the rectangular field are doubled, what would be the area of the doubled rectangular field?
- The doubled length:
[tex]\[
\text{Length doubled} = 2 \times 12 = 24 \, \text{meters}
\][/tex]
- The doubled breadth:
[tex]\[
\text{Breadth doubled} = 2 \times 8 = 16 \, \text{meters}
\][/tex]
- The area of the new, larger rectangle can be calculated as:
[tex]\[
\text{New Area} = 24 \, \text{meters} \times 16 \, \text{meters} = 384 \, \text{square meters}
\][/tex]
4. How many square tiles will be needed to cover the floor if the side of each tile is 60 cm?
- First, convert the side length of the tile from centimeters to meters:
[tex]\[
\text{Side of tile} = 60 \, \text{cm} = 0.6 \, \text{meters}
\][/tex]
- Calculate the area of one tile:
[tex]\[
\text{Area of one tile} = 0.6 \, \text{meters} \times 0.6 \, \text{meters} = 0.36 \, \text{square meters}
\][/tex]
- Determine the number of tiles needed to cover the floor:
[tex]\[
\text{Number of tiles} = \frac{\text{Area of the floor}}{\text{Area of one tile}} = \frac{96 \, \text{square meters}}{0.36 \, \text{square meters}}
\][/tex]
- Calculating this, we get:
[tex]\[
\text{Number of tiles} \approx 266.67
\][/tex]
Since you can't use a fraction of a tile in practice, you would need to round up to the next whole number, which means you would need 267 tiles to cover the floor.
So, to summarize the answers:
1. The length of the rectangular field is 12 meters.
2. The area of the rectangular floor is 96 square meters.
3. If the length and width of the rectangular field are doubled, the new area would be 384 square meters.
4. Approximately 267 square tiles (each with a side of 60 cm) would be needed to cover the floor.
