Question

Find the missing segment in the attached image

Answer 1

The length of the missing segment is 24

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;

`(15)/(x) = (15+5)/(8+x)`

`(15)/(x) = (20)/(8+x)`

Cross Multiply

`15 * (8 + x) = 20 * x`

Open bracket

`15*8 + 15 * x = 20 * x`

`120 + 15x = 20x`

Subtract 15x from both sides

`120 + 15x -15x= 20x-15x`

`120 = 20x-15x`

`120 = 5x`

Divide both sides by 5

`(120)/(5) = (5x)/(5)`

`(120)/(5) = x`

`24 = x`

`x = 24`

Hence, the length of the missing segment is 24