A rectangular plot measures 90 m by 50 m and is enclosed by a wire fence.\nFence poles are placed 5 m apart along the boundary (including poles at the corners).\nHow many poles are needed in total to complete the fencing?

Introduction:
This question tests perimeter calculation and equal spacing logic. When poles are placed at a fixed distance along a closed boundary, the total number of poles depends on the total length of the boundary (perimeter) divided by the spacing. Because the fencing forms a closed loop, the last point coincides with the starting point. If the perimeter is exactly divisible by the spacing and poles are placed at corners naturally, then the number of poles required equals perimeter/spacing. The key is to compute the perimeter correctly and interpret “5 m apart” properly for a closed fence.

Given Data / Assumptions:

• Length = 90 m
• Breadth = 50 m
• Spacing between poles = 5 m
• Rectangle perimeter P = 2(L + B)
• Fence is a closed loop around the rectangle

Concept / Approach:
Compute the perimeter first. Then divide by spacing to get the number of equal segments. In a closed loop with exact divisibility, number of poles equals number of segments because the final pole overlaps the starting position rather than adding an extra distinct pole.

Step-by-Step Solution:
Perimeter P = 2(90 + 50) = 2*140 = 280 mNumber of 5 m intervals around boundary = 280 / 5 = 56Therefore, total poles needed = 56

Verification / Alternative Check:
Along the 90 m side, poles create 90/5 = 18 intervals, and along 50 m side, 50/5 = 10 intervals. Total intervals around rectangle = 2*18 + 2*10 = 36 + 20 = 56 intervals, matching the perimeter method. Since each interval corresponds to one step from a pole to the next in a closed loop, the count of unique poles equals 56.

Why Other Options Are Wrong:
60 or 65 poles: would imply smaller spacing than 5 m or incorrect perimeter.34 or 36 poles: typically result from dividing only one side or forgetting to double for opposite sides.

Common Pitfalls:
Using area instead of perimeter.Forgetting perimeter includes all four sides.Adding 1 extra pole unnecessarily even when the fence is a closed loop and spacing divides exactly.Arithmetic mistake in 280/5.

Final Answer:
56 poles