Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. That tree can be seen when one walks 14 bu from the south gate, turns west and walks 1775 bu. Find the length of each side of the city.

The length of each side of the city is 250b

Step-by-step explanation:

Given

--- tree distance from north gate

--- movement from south gate

--- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

--- similar triangles

So, we have the following equivalent ratios

Where:

Substitute these in the above equation

Express as fraction

Cross multiply

Open bracket

Rewrite as:

Expand

Factorize

Factor out x + 284

Split

Solve for x

x can't be negative;

So:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)