For a project, Rishabh and Kavisha must measure a winding river drawn on a map
For a project, Rishabh and Kavisha must measure a winding river drawn on a map. Rishabh lays a straight ruler from one end of the river to the other and reads off the length. Kavisha lays a thread carefully along every bend of the river, marks where the river ends, then straightens the thread against the ruler. Whose method gives the river's real length on the map?
Who do you think is right? Pick one.
The answer: Kavisha is right, the thread follows every bend, a straight ruler doesn't
Why
Rishabh is correct that his ruler gives a real number — it is the straight-line distance between where the river starts and where it ends. But that is not the river's length. Water flowing down that river travels along every bend, and each bend adds extra length that a straight ruler skips over. A thread can follow the curve bend for bend, and once it is straightened out, an ordinary ruler can measure it. So the thread's length is always at least the straight distance, and for a very winding river it can be much longer. Test: draw a wavy line between two dots 10 cm apart, then lay a thread along it — the thread will measure clearly more than 10 cm. Kavisha is right: to measure a curved line, follow it with a thread and then measure the straightened thread.
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