A parallelogram has sides with lengths of #7 # and #16 #. If the parallelogram's area is #8 #, what is the length of its longest diagonal?

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Answer 1 · 2017-07-03T12:11:54

The length of the diagonal is #=22.99#

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Let #AB=16# and #AD=7#

The area of #ABCD# is

#A=AB*AD*sin hat(BAD)=8#

#sin hat(BAD)=8/(16*7)=1/14#

#hat(BAD)=4.1º#

Therefore,

#hat(ABC)=180-4.1=175.9º#

We apply the cosine rule to the triangle #ABC# to get the length of the longest diagonal #AC#

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

#=16^2+7^2-2*16*7*cos(175.9)#

#=528.4#

Therefore,

#AC=sqrt(528.4)=22.99#