A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #21 #, what is the length of its longest diagonal?

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Answer 1 · 2016-08-15T13:53:03

#=29#

Area of Parallelogram #=21=ab sintheta# where #a=14# and #b=15#
or
#21=14times15timessintheta#
or

#sin theta=21/14times1/15#
or
#sin theta=1/10#
or
#theta=sin^-1(1/10)#
or
#theta=5.74#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #5.74#

So we have Angle #180-5.74=174.26#

Using the Law of Cosine we can write
#y^2=14^2+15^2-2times14times15cos(174.26)#
#=196+225-2times14times15(-1)#
#=421+420#
#=841#
or
#y=sqrt841#

#=29#