Question

Find the missing segment in the attached image

Answer 1

The length of the missing segment is 44

Explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

`(20)/(x) = (10+20)/(22+x)`

`(20)/(x) = (30)/(22+x)`

Cross Multiply

`20 * (22 + x) = 30 * x`

Open bracket

`20 * 22 + 20 * x = 30 * x`

`440 + 20x = 30x`

Subtract 20x from both sides

`440 + 20x - 20x= 30x- 20x`

`440 = 30x- 20x`

`440 = 10x`

Divide both sides by 10

`(440)/(10) = (10x)/(10)`

`(440)/(10) = x`

`44 = x`

`x = 44`

Hence, the length of the missing segment is 44