Question

Geometry - No links please

Answer 1

36

Explanation:

`In\: \triangle ABR \:\&\: \triangle ANH`

BR || HN(Given)

Therefore,

`\angle ABR \cong \angle ANH` (Alternate angles)

`\angle BAR \cong \angle HAN` (Vertical angles)

`\therefore \triangle ABR \sim \triangle ANH` (AA postulate)

`\therefore (AB)/(AN) =(BR)/(HN)` (csst)

`\therefore (x)/(16) =(27)/(12)`

`\therefore (x)/(16) =(9)/(4)`

`\therefore x =(9* 16)/(4)`

`\therefore x ={9* 4}`

`\therefore x =36`