Chiu Chang Suann Jing/Examples/Example 7
Jump to navigation
Jump to search
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: Curious and Interesting Puzzles ... (previous) ... (next): The Nine Chapters: $65$