A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #44 #, what is the length of its longest diagonal?

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Answer 1 · 2017-07-12T12:28:23

The longest diagonal is #=19.5#

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Side #AB=DC=12#

Side #AD=BC=8#

The area of #ABCD# is

#AB*AD*sin hat(DAB)=44#

#sin hat(DAB)=44/(12*8)#

#hat(DAB)=27.3º#

The longest diagonal is #AC#

Angle #hat(ABC)=180-27.3=152.7º#

We apply the cosine rule to triangle #ABC#

#AC^2=AB^2+BC^2-2*AB*BC*cos hat(ABC)#

#=12^2+8^2-2*12*8*cos(152.7º)#

#=378.6#

Therefore,

#AC=sqrt378.6=19.5#