A parallelogram has sides with lengths of #16 # and #8 #. If the parallelogram's area is #80 #, what is the length of its longest diagonal?

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Answer 1 · 2016-03-23T08:51:56

longest diagonal #=22.8" "#units

From the given: two sides 16 and 8 and area=80, are enough to compute for the height h of the parallelogram.

Area = 16h
80=16h
#h=5#

Compute the larger interior angle: Let that angle be X

#X=180^@-sin^-1 (h/8)=180^@-38.6822^@=141.318^@#

Now using Cosine Law to compute the longer diagonal #d#

#d=sqrt(16^2+8^2-2*(16)*(8)*cos (141.318^@)#

#d=22.8" "#units

God bless...I hope the explanation is useful.