Two opposite sides of a parallelogram each have a length of #1 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #24 #, how long are the other two sides?

1 Answer
Oct 6, 2016

The other sides have a length of (approximately) #33.94# units

Explanation:

If you are getting a lot of these types of questions, it is useful to know that for a parallelogram with sides of length #L# and #W# and an interior angle of #theta#
#color(white)("XXX")"Area" = sin(theta) * L * W#

In this case using #theta=(3pi)/4# and #W=1# we have
#color(white)("XXX")24=sin((3pi)/4) * L * 1#

#color(white)("XXXX")=1/sqrt(2)L#

#color(white)("XXX")rarr L = 24sqrt(2)~~33.94#