A parallelogram has sides with lengths of #5 # and #9 #. If the parallelogram's area is #30 #, what is the length of its longest diagonal?

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Answer 1 · 2017-06-13T12:43:05

The length of the longest diagonal #=13.2#

The area of the parallelogram is

#A= a b sintheta#

Where,

#a# and #b# are the sides and

#theta# the angle between the sides

#5*9sintheta=30#

#sintheta=30/45=2/3#

#theta=41.81º#

To find the longest diagonal, we need the supplementary angle

#theta_1=180-41.81=138.19º#

Let the longest diagonal #=d#

We apply the cosine rule

#d^2=a^2+b^2-2*a*b*costheta_1#

#=5^2+9^2-2*5*9*cos(138.19º)#

#=25+81-90*(-0.745)#

#=173.08#

#d=sqrt173.08#

#=13.2#