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 = 10 chi = 100 cun. give your answers inunits of chi and cun.

Step-by-step explanation:

The factor-of-ten relationship between the different units means we can combine the numbers in decimal fashion. If 1 unit is 1 zhang, then 1 chi is 0.1 zhang and 1 cun is 0.01 zhang. Hence 6 chi 8 cun is 0.68 zhang.

Let x and y represent the width and height, respectively. In terms of zhang, we have ...

  y - x = 0.68

  x^2 +y^2 = 1^2

Substituting y = 0.68 +x into the second equation gives ...

  x^2 + (x +0.68)^2 = 1

  2x^2 +1.36x - 0.5376 = 0 . . . . . eliminate parentheses, subtract 1

Using the quadratic formula, we have ...

  x = (-1.36 ±√(1.36^2 -4(2)(-0.5376)))/(2·2) = (-1.36 ±√6.1504)/4

  x = 0.28 . . . . . the negative root is of no interest

  y = 0.28 +0.68 = 0.96

In units of chi and cun, the dimensions are ...

  height: 9 chi 6 cun

  width: 2 chi 8 cun

Height: 9 chi 6 cun

Width: 2 chi 8 cun

Step-by-step explanation:

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. The height of the door is  9 chi 6 cun  and the width of the door is 2 chi 8 cun.

1 zhang = 10 chi = 100 cun

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

hope it will

#faazmessi

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5