Complete question is;
Now there is a door whose height is more than its weight by 6 chi 8 cun. The distance is between the opposite is corners is 1 zhang. Find the height and width of the door.
Note: 1 zhange = 10 chi = 100 cun. Give your answers in units of chi and cun.
Answer:
h = 9 chi 6 cun
w = 2 chi 8 cun
Explanation:
Let the height be h and width be w.
Now, we are told that height is more than its weight by 6 chi 8 cun.
Thus,
weight = height - 6 chi 8 cun
Let's convert 6 chi 8 cun to chi for easy calculation.
Since 100 cun = 10 chu
Then 8 cun = 8 × 10/100 = 0.8 chi
Thus 6 chi 8 cun = 6 chi + 0.8 chi = 6.8 chi
Thus;
Height is h
Width is (h - 6.8) chi
Now, we are told that the distance between the corners is 1 zhang = 10 chi
Distance between corners is the diagonal of the door.
Thus, the height, width and diagonal con form a right angle triangle which can be solved by Pythagoreas theorem.
Thus;
h² + w² = 10²
Plugging in (h - 6.8) for w, we have;
h² + (h - 6.8)² = 100
h² + h² - 13.6h + 46.24 = 100
2h² - 13.6h + 46.24 - 100 = 0
2h² - 13.6h - 53.76 = 0
Using quadratic formula, we have;
h = 9.6 chi
Converting 0.6 chi to cun gives;
0.6 × 100/10 = 6 cun
Thus, h = 9 chi 6 cun
Since w = (h - 6 chi 8 chun)
Then, w = 9 chi 6 cun - 6 chi 8 chun = 2 chi 8 chun