Chiu Chang Suann Jing/Examples/Example 6

Example of Problem from

 * 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:

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