# Chiu Chang Suann Jing/Examples/Example 7

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## Example of Problem from

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

*A chain suspended from an upright post has a length of $2$ feet lying on the ground,**and on being drawn out to its full length, so as just to touch the ground,**the end is found to be $8$ feet from the post.*

*What is the length of the chain?*

## Solution

The chain is $17$ feet long.

## Proof

Let the height of the post be $h$.

The length of the chain is then $h + 2$.

When drawn out to its full length, the chain forms the hypotenuse of a right triangle.

One of the legs of that right triangle is the post, which is $h$ feet long.

The other leg is the distance of the end of the chain from the post, which is $8$ feet.

Hence:

\(\ds \paren {h + 2}^2\) | \(=\) | \(\ds h^2 + 8^2\) | Pythagoras's Theorem | |||||||||||

\(\ds \leadsto \ \ \) | \(\ds 4 h + 4\) | \(=\) | \(\ds 64\) | simplification | ||||||||||

\(\ds \leadsto \ \ \) | \(\ds h\) | \(=\) | \(\ds 15\) | simplification |

The right triangle in question here is the $\text{8-15-17}$ triangle.

$\blacksquare$

## Sources

- c. 100: Anonymous:
*Chiu Chang Suann Jing* - 1965: Henrietta Midonick:
*The Treasury of Mathematics: Volume $\text { 1 }$* - 1992: David Wells:
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