# Chiu Chang Suann Jing/Examples/Example 7

## 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.

$\blacksquare$