Measuring the River

measuring the river

A traveler reaches a river at the point A and wishes to know the width across to B. As he has no means of crossing the river, what is the easiest way of finding its width?

From Henry Dudeney.

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“Measure any convenient distance along the bank from A. to C, say 40 yards. Then measure any distance perpendicularly to D, say 12 yards. Now sight along DB and find the point E. You can then measure the distance from A to E, which will here be 24 yards, and from E to C, which will be 16 yards. Now AB:DC = AE:EC, from which it is evident that AB, the width of the river, must be 18 yards.”

August 31, 2008January 21, 2013 | Puzzles