A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?

### Concept & Formula The total length of the fence is the perimeter of the rectangle. For a closed continuous shape (like a fenced rectangle), the number of poles equals the total perimeter divided by the distance between consecutive poles. $$ \text{Perimeter} = 2(L + B) $$ $$ \text{Number of poles} = \frac{\text{Total Perimeter}}{\text{Spacing}} $$ ### Step-by-Step Solution * **Given:** Length = $90\text{ m}$, Breadth = $50\text{ m}$, Spacing = $5\text{ m}$. * **Step 1:** Calculate the perimeter of the plot. $\text{Perimeter} = 2 \times (90 + 50)$ $\text{Perimeter} = 2 \times 140 = 280\text{ m}$ * **Step 2:** Calculate the number of poles. $\text{Poles} = \frac{280}{5}$ $\text{Poles} = 56$ ### Exam Strategy & Shortcut To divide any number by $5$ quickly, double the number and divide by $10$. Here, $280 \times 2 = 560$, and $560 / 10 = 56$. ### Common Pitfall A common mistake is treating this like a straight line problem and adding $1$ to the final count (i.e., calculating $56 + 1 = 57$). Remember that in a closed loop, the starting pole and ending pole are the exact same pole, so you do not add $1$. ### Final Answer Therefore, the correct answer is **56**.