# Chiu Chang Suann Jing/Examples/Example 6

Jump to navigation
Jump to search
## Example of Problem from

## Example of Problem from *Chiu Chang Suann Jing*

*There is a pool $10$ feet square, with a reed growing vertically in the centre,**its roots at the bottom of the pool, which rises $1$ foot above the surface;**when drawn towards the shore it reaches exactly to the brink of the pool;*

*what is the depth of the water?*

## Solution

The water is $12$ feet deep.

## Proof

Let the depth of the water be $d$.

The length of the reed is $d + 1$.

When drawn to the edge of the pool, the reed forms the hypotenuse of a right triangle.

One of the legs of that right triangle is the depth of the pool, which is $d$.

The other leg is the distance from the centre of the pool, which is $5$ feet.

Hence:

\(\ds \paren {d + 1}^2\) | \(=\) | \(\ds d^2 + 5^2\) | Pythagoras's Theorem | |||||||||||

\(\ds \leadsto \ \ \) | \(\ds 2 d + 1\) | \(=\) | \(\ds 25\) | simplification | ||||||||||

\(\ds \leadsto \ \ \) | \(\ds d\) | \(=\) | \(\ds 12\) | simplification |

The right triangle in question here is the $\text{5-12-13}$ triangle.

$\blacksquare$

## Sources

- c. 100: Anonymous:
*Chiu Chang Suann Jing* - 1965: Henrietta Midonick:
*The Treasury of Mathematics: Volume $\text { 1 }$* - 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): The Nine Chapters: $64$