A parallelogram has sides with lengths of #7 # and #16 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-26T13:32:57

#=22.8#

Area of Parallelogram #=32=ab sintheta# where #a=7# and #b=16#
or
#32=7times16timessintheta#
or

#sin theta=32/16times1/7#
or
#sin theta=2/7#
or
#theta=sin^-1(2/7)#
or
#theta=16.6#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #16.6#

So we have Angle #180-16.6=163.4#

Using the Law of Cosine we can write
#y^2=7^2+16^2-2times7times16cos(163.4)#

#=49+256-2times7times16(-0.96)#

#=305+214.66#

#=519.66#
or
#y=sqrt519.66#

#=22.8#