Question

Geometry - No links please

Answer 1

Answer:

36

Step-by-step 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)

$\therefore \frac{AB}{AN} =\frac{BR}{HN}$ (csst)

$\therefore \frac{x}{16} =\frac{27}{12}$

$\therefore \frac{x}{16} =\frac{9}{4}$

$\therefore x =\frac{9\times 16}{4}$

$\therefore x ={9\times 4}$

$\therefore x =36$