Longest Rod Across a Rectangular Park — Diagonal Length: A park measures 10 m by 8 m. What is the length of the longest pole (rod) that can be placed flat inside the park?

Introduction / Context:
The longest straight object that can fit inside a rectangle lies along its diagonal. Therefore, the maximum pole length equals the rectangle's diagonal obtained by the Pythagorean theorem using the side lengths as perpendicular legs.

Given Data / Assumptions:

• Length = 10 m
• Breadth = 8 m
• Right-angle corner implies Pythagoras applies

Concept / Approach:
For a rectangle with sides a and b, the diagonal d satisfies d^2 = a^2 + b^2. Compute the square root of the sum of squares to find d. This geometric maximum is independent of object orientation as any longer orientation would exceed the rectangle's bounds.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 10 m equals one side, not the diagonal.
• 18 m far exceeds the rectangular dimension constraints.
• 12 m underestimates the true diagonal length.

Common Pitfalls:

• Forgetting that the diagonal is longer than either side but not longer than the hypotenuse computed via Pythagoras.
• Rounding early; carry enough precision before final rounding.

Final Answer:
12.8 metres.