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A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #150 #, what is the length of its longest diagonal?

Answer 1

Claire Akin

#=23.8#

Area of Parallelogram #=150=ab sintheta# where #a=15# and #b=12# or #150=15times12timessintheta# or

#sin theta=150/12times1/15# or #sin theta=5/6# or #theta=sin^-1(5/6)# or #theta=56.44#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #56.44#

So we have Angle #180-56.44=123.56#

Using the Law of Cosine we can write #y^2=15^2+12^2-2times15times12cos(123.56)# #=225+144-2times15times12(-0.55)# #=369+198# #=567# or #y=sqrt567# #=23.8#

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Answer from HIX Tutor

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