Two opposite sides of a parallelogram have lengths of #25 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #45 #, how long are the other two sides?

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Answer 1 · 2017-04-09T10:44:26

The length of the second side is #(9sqrt(2))/5#. See explanation.

In this task we have the area, one side and one angle of a paralellogram given.

One of methods of calculating the area is using the formula:

#A=axxbxxsin alpha#

where:
#a,b# are lengths of sides,

#alpha# is one of paralellogram's angles

After transforming this formula we get:

After substituting the given values we get:

#b=45/(25xxsin45)=45/(25sqrt(2)/2)=45 -: (25sqrt(2))/2#

#b=45xx2/(25sqrt(2))=90/(25sqrt(2))=18/(5sqrt(2))=#

#=(18sqrt(2))/10=(9sqrt(2))/5#