A parallelogram has sides with lengths of #14 # and #12 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-14T09:08:34

#=26#

Area of Parallelogram #=24=ab sintheta# where #a=14# and #b=12#
or
#24=14times12timessintheta#
or

#sin theta=24/14times1/12#
or
#sin theta=1/7#
or
#theta=sin^-1(1/7)#
or
#theta=8.2#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #8.2#

So we have Angle #180-8.2=171.8#

Using the Law of Cosine we can write
#y^2=14^2+12^2-2times14times12cos(171.8)#
#=196+144-2times14times12(-1)#
#=340+336#
#=676#
or
#y=sqrt676#

#=26#