A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #64 #, what is the length of its longest diagonal?

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Answer 1 · 2018-05-21T14:23:25

longest diagonal =12.00053677

If we split the parallelogram into using the smaller diagonal, the area would be 32 # cm^2#

using Area=#1/2 xxa xxb xxsin C#

#32=1/2xx8xx12xxsin theta#

#sin theta=32/48=2/3#

#theta=sin^(-1) [2/3]#

#theta=41.8^@#

Therefore the other angle is #180-41.8=138.2^@#

Using the cosine rule to find the longest diagonal

#a^2=b^2+c^2-sxxbxxcxxcosA#

#a^2=12^2+8^2-12xx8xxsin 138.2^@#

#a^2=208-96sin138.2^@#

#a^2=144.0128829#

a=12.00053677