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?

1 Answer
Jun 20, 2016

It is 16.55.

Explanation:

made with GeoGebramade 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.