Forty tiles of dimension 1 foot × 2 foot each are required to completely cover a floor. How many tiles of dimensions 2 foot `xx` 4 foot each would be required to completly cover the same floor?

Options

A. 10
B. 20
C. 80
D. 160

Answer

To solve the problem, we need to determine how many tiles of dimensions 2 feet by 4 feet are required to cover the same area that 40 tiles of dimensions 1 foot by 2 feet cover.

**Step 1: Calculate the area covered by the 40 tiles of dimension 1 foot × 2 foot.**

The area of one tile is:
\[ \text{Area of one tile} = \text{length} \times \text{width} = 1 \text{ foot} \times 2 \text{ feet} = 2 \text{ square feet} \]

Now, the total area covered by 40 tiles is:
\[ \text{Total area} = \text{Area of one tile} \times \text{Number of tiles} = 2 \text{ square feet} \times 40 = 80 \text{ square feet} \]

**Step 2: Calculate the area of one tile of dimension 2 feet × 4 feet.**

The area of one tile is:
\[ \text{Area of one tile} = \text{length} \times \text{width} = 2 \text{ feet} \times 4 \text{ feet} = 8 \text{ square feet} \]

**Step 3: Calculate the number of tiles required to cover the same area of 80 square feet.**

We can find the number of tiles required by dividing the total area by the area of one tile:
\[ \text{Number of tiles required} = \frac{\text{Total area}}{\text{Area of one tile}} = \frac{80 \text{ square feet}}{8 \text{ square feet}} = 10 \]

Thus, the number of tiles of dimensions 2 feet by 4 feet required to cover the same floor area is **10 tiles**.