Number of fence poles around a rectangle A rectangular plot measures 90 m by 50 m. It is to be enclosed by a wire fence with poles placed every 5 m (all around). How many poles are needed?

Introduction / Context:When equally spaced poles are placed around a closed loop with total length a multiple of the spacing, the count equals total length divided by the spacing.

Given Data / Assumptions:

• Length = 90 m, Breadth = 50 m ⇒ Perimeter P = 2*(90 + 50) = 280 m
• Spacing = 5 m
• Perimeter is an exact multiple of spacing.

Concept / Approach:If P is divisible by the spacing, number of poles N = P / spacing (because start and end coincide on a looped fence).

Step-by-Step Solution:

Verification / Alternative check:Positions every 5 m around 280 m yield exactly 56 intervals/poles, closing the loop without overlap.

Why Other Options Are Wrong:45, 55, and 65 do not equal the exact division result for a multiple-of-5 perimeter.

Common Pitfalls:Double-counting the initial pole or assuming an extra pole at closure; when P is a multiple of spacing, simple division suffices.

Final Answer:56