A parallelogram has sides with lengths of #12 # and #6 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-16T11:52:45

#=17.23#

Area of Parallelogram #=42=ab sintheta# where #a=12# and #b=6#
or
#42=12times6timessintheta#
or

#sin theta=42/12times1/6#
or
#sin theta=7/12#
or
#theta=sin^-1(7/12)#
or
#theta=35.7#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #35.7#

So we have Angle #180-35.7=144.3#

Using the Law of Cosine we can write
#y^2=12^2+6^2-2times12times6cos(144.3)#
#=144+36-2times12times6(-0.812)#
#=180+117#
#=297#
or
#y=sqrt297#

#=17.23#