A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #81 #, what is the length of its longest diagonal?

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Answer 1 · 2017-07-19T07:31:07

The length of the longest diagonal is #=26.8u#

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The dimensions of the parrallelogram are

#AB=15#

#AD=12#

The #area=81#

But the area of a parallelogram is

#area=AB*AD*sin hatA#

#15*12*sin hatA=81#

#sin hat A=81/(15*21)=0.257#

#hatA=14.9^@#

The longest diagonal is #=AC#

We apply the cosine rule to the triangle #DeltaABC#

#AC^2=AB^2+BC^2-2*A*B*cos(180^@-14.9^@)#

#=15^2+12^2-2*15*12*cos(165.1^@)#

#=716.9#

#AC=sqrt716.9=26.8#