A parallelogram has sides with lengths of #12 # and #4 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

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Answer 1 · 2017-02-13T11:12:56

The length of the longest diagonal is #=sqrt(160+24sqrt7)#

We have a parallelogram #ABCD#

#AD=4#

#AB=12#

Area = base x height

#36=12*h#

#h=3#

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The distance between the base of the height and the corner #D# is

#=sqrt(AD^2-h^2)=sqrt(16-9)=sqrt7#

Therefore,

#DB^2=h^2+(DC+sqrt7)#

#DB^2=9+(12+sqrt7)^2#

#DB^2=9+144+7+24sqrt7#

#DB^2=160+24sqrt7#

#DB=sqrt(160+24sqrt7)#