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?

The chain is $17$ feet long.

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:

$\ds \paren {h + 2}^2$

$=$

$\ds h^2 + 8^2$

$\ds \leadsto \ \ $

$\ds 4 h + 4$

$=$

$\ds 64$

simplification

$\ds \leadsto \ \ $

$\ds h$

$=$

$\ds 15$

simplification

$\blacksquare$