A parallelogram has sides with lengths of #16 # and #15 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-14T09:37:29

#=31#

Area of Parallelogram #=48=ab sintheta# where #a=16# and #b=15#
or
#48=16times15timessintheta#
or

#sin theta=48/16times1/15#
or
#sin theta=1/5#
or
#theta=sin^-1(1/5)#
or
#theta=11.54#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #11.54#

So we have Angle #180-11.54=168.46#

Using the Law of Cosine we can write
#y^2=16^2+15^2-2times16times15cos(168.46)#
#=256+225-2times16times15(-1)#
#=481+480#
#=961#
or
#y=sqrt961#

#=31#