Question

The triangles are similar. Find the missing length x.

Answer 1

36

Explanation:

If the triangles have similar sides, any increase or decrease in side length is in equal number. This means equal ratio. How?

Let the common factor of decrease in side OD to AP be, z

`(30)/(20) = z`

And, the common factor of decrease in side DT to PN be, z

`(x)/(24) = z`

So,
`z = z`

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

`(30)/(20)` ×
`24` =
`{x}`

Therefore,

`{x}` =
`(3)/(2)` ×
`24`

=
`3` ×
`12`

=
`36`