Find the maximum distance between two points on the perimeter of a rectangular field whose length and breadth are 80 m and 60 m.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 100 m
The two points of a rectangle that are farthest apart are opposite corners, so the maximum distance is the length of the diagonal. The diagonal and two sides form a right triangle, so Pythagoras’ theorem gives it.
\(AC^{2}=80^{2}+60^{2}=6400+3600=10000\)
\(AC=\sqrt{10000}=\) 100 m
Why the other options are incorrect
Option (1) 70 m — Incorrect. This is only the average of the two sides, not a distance across the field.
Option (3) 140 m — Incorrect. This is the walk along two sides (80 + 60), not the straight distance between the corners.
Option (4) 4800 m — Incorrect. \(80\times60=4800\) is the area of the field in square metres.