Answer:
36
Step-by-step explanation:
[tex] In\: \triangle ABR \:\&\: \triangle ANH[/tex]
BR || HN(Given)
Therefore,
[tex] \angle ABR \cong \angle ANH[/tex] (Alternate angles)
[tex] \angle BAR \cong \angle HAN[/tex] (Vertical angles)
[tex] \therefore \triangle ABR \sim \triangle ANH[/tex] (AA postulate)
[tex] \therefore \frac{AB}{AN} =\frac{BR}{HN} [/tex] (csst)
[tex] \therefore \frac{x}{16} =\frac{27}{12} [/tex]
[tex] \therefore \frac{x}{16} =\frac{9}{4} [/tex]
[tex] \therefore x =\frac{9\times 16}{4} [/tex]
[tex] \therefore x ={9\times 4} [/tex]
[tex] \therefore x =36 [/tex]
