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

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.

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

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!