Question

Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang. Find the height and width of the door.NOTE: 1 zhang

Answer 1

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

Step-by-step 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