Why did Viola dress-up as a boy/her brother?
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Viola never precisely says why she decides to dress up as a boy. But a reasonable guess is that she knows Olivia won't be hiring (Olivia is in mourning - she doesn't get out much) and it will be easier to get a manservant job with Duke Orsino.
There is an interesting essay on this theme in John Sutherland "Was Henry V a War Criminal?". Perhaps your school has it.
The dramatic reason is that because all female roles were played by young boys on the Elizabethan stage, Shakespeare loved genderbending his female characters.
Viola dreeses up like her brother so that she can take on a position in Duke Orsino's household (court).