A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #18 #, what is the length of its longest diagonal?

1 Answer
May 8, 2016

Find the height. Use Pythagoras twice: to find how far the base extends, and then to find the length of the longer diagonal.
#d = 16.86#

Explanation:

Draw a sketch of the parallelogram first!

Find the height of the parallelogram. A = b x h

#h = A/b = 18/9 =2#

The endpoint of the top line of the parallelogram is vertically above the base extended.
We need to calculate the length of the extended line, let's call it #x#.

Working in the right-angled triangle outside the parallelogram with
Hypotenuse = 8 and height = 2 , gives the following:

#x^2 = 8^2 - 2^2 = 60#
#x = sqrt60 " "# leave it in this form

Length of the extended base = #9 + sqrt60~~16.746....#

Now work with the right-angled triangle with the longer diagonal# (d)# as the hypotenuse, and the two shorter sides being #2 and (9+sqrt60)#

#d^2 = (9+sqrt60)^2 +2^2 =284.427....#

#d = 16.86#