A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

Question

1234 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-20T13:51:48

It is #16.55#.

made with GeoGebra

Consider the image. From the initial data we have

#A=9, B=8#, the area is #32#.
We know that the area is #A*h# so we have

#A*h=32# and then

#h=32/9=3.\bar{5}#

For the longest diagonal we need to know #C# that is

#C=sqrt(B^2-h^2)=sqrt(8^2-3.\bar{5}^2)\approx7.166#

Finally, the diagonal is

#D=sqrt((A+C)^2+h^2)=sqrt((9+7.166)^2+3.\bar{5}^2)#

#=sqrt(16.166^2+3.\bar{5}^2)\approx16.55#.