A rectangular plot measures 90 metres in length and 50 metres in breadth. It is to be completely enclosed by a wire fence, and fence poles are to be placed at intervals of 5 metres along the boundary. How many fence poles are required in total?

Introduction:
This is a perimeter and spacing problem involving a rectangular plot surrounded by fence poles placed at equal intervals. Such questions are very common in aptitude exams to test understanding of perimeter, regular spacing, and careful counting of points on a closed boundary. The key is to calculate the total boundary length and then decide how many poles are needed if they are placed every fixed distance along that boundary.

Given Data / Assumptions:

• Length of the rectangular plot = 90 metres. • Breadth of the rectangular plot = 50 metres. • Distance between consecutive fence poles = 5 metres. • Poles are placed along the entire perimeter of the rectangle.

Concept / Approach:
The total length of the boundary of the rectangle is its perimeter. For a rectangle, perimeter = 2 * (length + breadth). Once we know the perimeter, we divide this length by the spacing between the poles to find how many segments of that length fit around the boundary. For equally spaced poles on a circular or closed path, each spacing corresponds to the distance between two consecutive poles, and the number of such spacings is equal to the number of poles if we complete the loop exactly.

Step-by-Step Solution:
Step 1: Compute perimeter of the rectangle. Perimeter = 2 * (length + breadth) = 2 * (90 + 50). Step 2: Add the sides inside the bracket. 90 + 50 = 140, so perimeter = 2 * 140 = 280 metres. Step 3: Compute the number of intervals of 5 metres along the boundary. Number of intervals = perimeter / spacing = 280 / 5. Step 4: Perform the division. 280 / 5 = 56. Step 5: Interpret the result. Each 5 metre interval corresponds to the distance between two consecutive poles. On a complete loop, the number of intervals equals the number of poles, so 56 poles are required.

Verification / Alternative check:
If we imagine walking along the boundary, starting at one corner and placing a pole there, then placing another pole every 5 metres, after 56 such steps we would come back to the starting point exactly because 56 * 5 = 280 metres, which matches the perimeter. This confirms that there is no need for an extra pole and that 56 is the correct total count of poles around the rectangle.

Why Other Options Are Wrong:
Option 65 poles: This is larger than required and would imply a total length greater than the perimeter. Option 55 poles: This would give a total covered length of 55 * 5 = 275 metres, leaving 5 metres of boundary without a pole. Option 45 poles: This is far too small and would not cover the whole perimeter. Option 60 poles: This would mean 60 * 5 = 300 metres of fencing, which exceeds the perimeter and is not possible with a 5 metre spacing on a 280 metre boundary.

Common Pitfalls:
A typical mistake is adding one extra pole by thinking that the starting point must be counted separately, leading to perimeter/spacing + 1. This is not correct when the total perimeter is exactly a multiple of the spacing, because the last pole placed at the final 5 metre step coincides with the starting corner. Another mistake is to miscalculate the perimeter due to incorrect addition of the sides.

Final Answer:
The number of fence poles required is 56 poles.