Finding the Vertical Side from its Difference

[Diagram: A top-down view of a double-leaf door shown slightly ajar. The two doors meet at an angle, leaving a trapezoidal gap between the door frame and the doors. Labels indicate the measurements for the "base" and "vertical side" of the resulting triangle.] Gap: 2 units Distance of separation Vertical Side (Gu): 4 feet 9.5 inches Base (Gou): 10 inches 1 foot | 1 foot

The answer says: The width of the two door leaves combined is 9 feet 9 inches.

The method says: Take the opening width of 10 inches 10 as the base 勾 (Gou): the shorter leg of a right triangle. Multiply it by itself to get 100 100. Take the gap of 2 2 where the doors do not meet and halve it to get 1 1; this is the vertical difference 股較 (Gu Jiao): the difference between the hypotenuse and the vertical side. Multiply this difference by itself to get 1 1. Subtract this from 100 100 to get a remainder of 99 99, which is the dividend 實 (Shi): the number to be divided. Double the difference of 1 1 to get 2 2, which is the divisor 法 (Fa): the number used to divide. Divide the dividend by this; the result is 4 feet 9.5 inches 4 feet 9.5 inches, which is the width of one door leaf, acting as the vertical side 股 (Gu): the longer leg of a right triangle. Double this to get the width of both door leaves: 9 feet 9 inches 9 feet 9 inches. This matches the question.

Suppose there is a wall 10 feet original: "1 zhang." high. Two pieces of timber are leaned against the top so that the tips of the timbers are flush with the top of the wall. The base of the timbers rests on the ground. Now, if one timber is laid flat on the ground with its tip touching the foot of the wall, its base extends 1 foot beyond the base of the slanted timber. Ask: what is the length of the timber and its distance from the wall?