A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #63 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-18T16:10:54

#=15.35#

Area of Parallelogram #=63=ab sintheta# where #a=9# and #b=8#
or
#63=9times8timessintheta#
or

#sin theta=63/72#
or
#sin theta=7/8#
or
#theta=sin^-1(7/8)#
or
#theta=61#

To find the longer diagonal #=y=?#

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

So we have Angle #180-61=129#

Using the Law of Cosine we can write
#y^2=9^2+8^2-2times9times8cos(129)#

#=81+64-2times9times8(-0.63)#

#=145+90.72#

#=235.72#
or
#y=sqrt235.72#

#=15.35#