Answer:
88 units
Step-by-step explanation:
[tex] In\: \triangle OBR \:\&\: \triangle OWN[/tex]
BR || WN (Given)
Therefore,
[tex] \angle OBR \cong \angle OWN[/tex] (Alternate angles)
[tex] \angle BOR \cong \angle WON[/tex] (Vertical angles)
[tex] \therefore \triangle OBR \sim \triangle OWN[/tex] (AA postulate)
[tex] \therefore \frac{OR}{ON} =\frac{BR}{WN} [/tex] (csst)
[tex] \therefore \frac{OR}{56} =\frac{24}{42} [/tex]
[tex] \therefore \frac{OR}{56} =\frac{4}{7} [/tex]
[tex] \therefore OR =\frac{4\times 56}{7} [/tex]
[tex] \therefore OR ={4\times 8} [/tex]
[tex] \therefore OR =32 [/tex]
RN = OR + ON
RN = 32 + 56
RN = 88 units
