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?

1 Answer
Aug 12, 2016

#=23.8#

Explanation:

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#