Question

A parallelogram has sides with lengths of `16` and `15`. If the parallelogram's area is `8`, what is the length of its longest diagonal?

Answer 1

`d=sqrt(481+16sqrt(899))=30.9957...`

Explanation:

Let `h_a` be the height relative to side `a=16`

Then
`A=h_a*a`
so
`8=h_a*16`
and
`h_a=1/2`

Then the projection of b on a is

`p_b=sqrt(15^2-1/2^2)=sqrt(899)/2`

Finally the diagonal is

`d=sqrt( (16+sqrt(899)/2)^2+1/2^2)=sqrt(481+16sqrt(899))`