Henry Ernest Dudeney/Puzzles and Curious Problems/200 - Measuring the River/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $200$

Measuring the River

A traveller 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?

Solution

The initial assumption is made that it is possible to identify features on the opposite bank of the river, and to identify when one is exactly opposite such a feature.

It is also assumed that the traveller has the basic surveying apparatus necessary.

We have been given that $A$ is directly opposite point $B$, which can thus be identified.

Measure an arbitrary distance $AC$ along the river bank perpendicular to $AB$.

Then measure another arbitrary distance $CD$ similarly perpendicular to $AC$.

Then locate the point $E$, which is where $AC$ and $DB$ cross.

The triangles $\triangle ABE$ and $\triangle CDE$ are then similar.

The distance $AB$ can then be determined by elementary geometry.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $200$. -- Measuring the River
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $306$. Measuring the River