Babylonian Mathematics/Examples/Sliding Ladder

Example of Babylonian Mathematics
A ladder of length $0; 30$ stands upright against a wall.

The upper end slides down a distance $0; 6$.

How far away will the lower end move out from the wall?

All lengths are expressed in Babylonian form.

Solution
The lower end of the ladder will move $0; 18$ away from the wall.

Proof
The ladder will be the hypotenuse of a right triangle whose legs are formed by the wall and the floor.

Let $x$ be the distance of the lower end from the wall after the ladder has finished moving.

We have: