A square tile has side 30 cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?

1. Analyze the question

We need to find the number of square tiles required to cover a rectangular floor. To do this, we must divide the total area of the floor by the area of a single tile. Crucially, we must ensure all units are consistent (converting meters to centimeters).

2. Explain the concept

• Area of a rectangle: Length × Width
• Area of a square: Side × Side
• Number of tiles: (Total Area of Floor) / (Area of One Tile)
• Unit Conversion: Since the tile is in centimeters (cm) and the floor is in meters (m), we convert meters to centimeters: $1\text{ m} = 100\text{ cm}$.

3. Show the solution

Step 1: Convert floor dimensions to centimeters

• Length = $7.2\text{ m} = 7.2 \times 100 = 720\text{ cm}$
• Width = $4.2\text{ m} = 4.2 \times 100 = 420\text{ cm}$

Step 2: Calculate the area of the floor

• Area of floor = $720\text{ cm} \times 420\text{ cm} = 302,400\text{ cm}^2$

Step 3: Calculate the area of one tile

• Area of tile = $30\text{ cm} \times 30\text{ cm} = 900\text{ cm}^2$

Step 4: Calculate the number of tiles needed

• Number of tiles = $\frac{\text{Total Area}}{\text{Tile Area}}$
• Number of tiles = $\frac{302,400}{900}$
• Cancel the zeros: $\frac{3024}{9}$
• $3024 \div 9 = 336$

4. Identify the answer

The calculation confirms that 336 tiles are required to cover the floor. This matches option B.

5. Tip

Always check your units first! A common mistake in JAMB Mathematics is calculating using mixed units (meters and centimeters). Converting everything to the smaller unit (cm) at the very beginning prevents silly errors. Also, notice that $\frac{720}{30} \times \frac{420}{30}$ gives the same result ($24 \times 14 = 336$); this is a faster way to solve it by finding how many tiles fit along the length and width separately!