A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

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Answer 1 · 2017-06-17T09:19:10

The length of the longest diagonal is #=32.92#

The area of the parallelogram is

#A=ab sintheta#

#a=21#

#b=12#

#A=36#

#sintheta=A/(ab)=36/(12*21)=1/7#

#theta=arcsin(1/7)=8.21º#

The supplementary angle is #=180-8.21=171.79º#

To find the longest diagonal #d#, we apply the cosine rule

#d^2=a^2+b^2-2abcos(180-theta)#

#d^2=21^2+12^2-2*21*12*cos171.79#

#d^2=1083.8#

#d=32.92#