A parallelogram has sides with lengths of #18 # and #3 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-22T20:37:08

#=20.35#

Area of Parallelogram #=36=ab sintheta# where #a=18# and #b=3#
or
#36=18times3timessintheta#
or

#sin theta=36/54#
or
#sin theta=2/3#
or
#theta=sin^-1(2/3)#
or
#theta=41.8#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #41.8#

So we have Angle #180-41.8=138.2#

Using the Law of Cosine we can write
#y^2=18^2+3^2-2times18times3cos(138.2)#

#=324+9-2times18times3(-0.75)#

#=333+108(0.75)#

#=333+81#

#=414#
or
#y=sqrt414#

#=20.35#