A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

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Answer 1 · 2017-02-19T08:55:38

The longest diagonal is #=33#

We have a parallelogram #ABCD#

#AD=12#

#AB=21#

Area = base x height

#24=21*h#

#h=24/21=8/7#

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

#=sqrt(AD^2-h^2)=sqrt(144-64/49)=sqrt(6992/49)=11.95#

Therefore,

#DB^2=h^2+(DC+11.95)^2#

#DB^2=64/49+(21+11.95)^2#

#DB^2=64/49+1085.7#

#DB^2=1087#

#DB=sqrt1087#

#DB=33#