A parallelogram has sides with lengths of #14 # and #9 #. If the parallelogram's area is #56 #, what is the length of its longest diagonal?

1 Answer
Aug 12, 2016

#=22.45#

Explanation:

Area of Parallelogram #=56=ab sintheta# where #a=14# and #b=9#
or
#56=14times9timessintheta#
or

#sin theta=56/14times1/9#
or
#sin theta=4/9#
or
#theta=sin^-1(4/9)#
or
#theta=26.4#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #26.4#

So we have Angle #180-26.4=153.6#

Using the Law of Cosine we can write
#y^2=14^2+9^2-2times14times9cos(153.6)#
#=196+81-2times14times9(-0.9)#
#=196+81+226.8#
#=504#
or
#y=sqrt504#
#=22.45#