Renu wants to lay tiles on the floor of her house which is 9 m long and 7 m wide. Among the following sizes of tiles, which one should she buy, so that the floor is tiled without cutting any tile?

Options

A. `40cmxx65cm`
B. `55 cm xx 40 cm`
C. `35 cmxx 45cm`
D. `35 cm xx 35 cm`

Answer

To determine which size of tiles Renu should buy to cover her floor without cutting any tiles, we need to follow these steps:

### Step 1: Calculate the Area of the Floor
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

Given:
- Length = 9 m
- Width = 7 m

Calculating the area:
\[ \text{Area} = 9 \, \text{m} \times 7 \, \text{m} = 63 \, \text{m}^2 \]

### Step 2: Convert the Area to Square Centimeters
Since tile sizes are often given in square centimeters, we need to convert the area from square meters to square centimeters.
1 square meter = 10,000 square centimeters.

Calculating the area in square centimeters:
\[ \text{Area} = 63 \, \text{m}^2 \times 10,000 \, \text{cm}^2/\text{m}^2 = 630,000 \, \text{cm}^2 \]

### Step 3: Determine the Dimensions of the Floor in Centimeters
Convert the dimensions of the room to centimeters:
- Length = 9 m = 900 cm
- Width = 7 m = 700 cm

### Step 4: Find the Factors of the Area
To find suitable tile sizes, we need to find the factors of the area (630,000 cm²). The tile dimensions must be factors of both the length and width of the floor.

### Step 5: List Possible Tile Sizes
We need to find the factors of 900 cm and 700 cm. The common factors will give us the possible sizes of tiles that can be used without cutting.

- Factors of 900: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
- Factors of 700: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

### Step 6: Identify Common Factors
The common factors of 900 and 700 will give us the possible tile dimensions:
- Common factors: 1, 2, 5, 10, 14, 20, 25, 35, 50, 70, 100

### Step 7: Choose the Largest Common Factor
To minimize the number of tiles needed, Renu should choose the largest common factor. The largest common factor from the list is 100.

### Conclusion:
Renu should buy tiles that are 100 cm x 100 cm in size to cover her floor without cutting any tiles.

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