How many metres of carpet 63 cm wide will be required to cover the floor of a room 14 m by 9 m? (R.R.B. ,2008)

### Concept & Area Equivalence When covering a floor with a roll of carpet, the total surface area of the unrolled carpet must equal the surface area of the floor. $$ \text{Area of Carpet} = \text{Area of Floor} $$ $$ \text{Length of Carpet} \times \text{Width of Carpet} = \text{Length of Room} \times \text{Breadth of Room} $$ ### Step-by-Step Solution 1. **Calculate the area of the room's floor:** $$ \text{Length of floor} = 14 \text{ m} $$ $$ \text{Breadth of floor} = 9 \text{ m} $$ $$ \text{Area of floor} = 14 \times 9 = 126 \text{ m}^2 $$ 2. **Standardize the width of the carpet:** The width of the carpet is given as $63 \text{ cm}$. Convert this to meters to match the floor area unit. $$ \text{Width} = \frac{63}{100} = 0.63 \text{ m} $$ 3. **Equate the areas to find the required length:** Let the required length of the carpet be $L$ meters. $$ L \times 0.63 = 126 $$ 4. **Solve for L:** $$ L = \frac{126}{0.63} $$ $$ L = \frac{126 \times 100}{63} $$ $$ L = 2 \times 100 = 200 \text{ m} $$ ### Exam Strategy & Shortcut Set up the fraction before multiplying anything out: $L = \frac{14 \times 9}{0.63}$. Notice that $14 \times 9$ involves multiples of $7$ and $9$, which are exactly the prime factors of $63$. You can simplify immediately: $0.63 = 9 \times 0.07$. Cancel the $9$, leaving $\frac{14}{0.07} = \frac{1400}{7} = 200$. ### Common Pitfall Forgetting to convert the carpet width from centimeters to meters is a primary trap. This error will result in calculating an area mismatch and an incorrect length magnitude. ### Final Answer Therefore, the correct answer is **200 m**.