Two opposite sides of a parallelogram each have a length of #1 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #5 #, how long are the other two sides?

1 Answer
Mar 12, 2017

#5sqrt(2)#

Explanation:

Let us call this parallelogram #ABCD#, and the unknown lengths (#AD# and #BC#) #x#. Given that one angle (say #B#) is #frac(3pi)(4)#, or #135# degrees, the supplementary angle (or #A#) in the parallelogram is #45# degrees. Then, draw down the height to #AD#. Because #angleA=45#, then the height is #frac(1)(sqrt(2))#. Now we know the height (#frac(1)(sqrt(2))#) and the base (which we declared as #x#). Since the area of a parallelogram is #A=bh#, #5=xfrac(1)(sqrt(2))#. So, the unknown length is simply #5sqrt(2)#.