Question

Find the missing segment in the attached image

Answer 1

The length of the missing segment is 36

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)/(24) = (30+20)/(24+x)`

`(20)/(24) = (50)/(24+x)`

Cross Multiply

`20 * (24 + x) = 24 * 50`

`20 * (24 + x) = 1200`

Divide both sides by 20

`(20 * (24 + x))/(20) = (1200)/(20)`

`(24 + x)= (1200)/(20)`

`24 + x= 60`

Subtract 24 from both sides

`24 - 24 + x = 60 - 24`

`x = 60 - 24`

`x = 36`

Hence, the length of the missing segment is 36