Question

A parallelogram has sides with lengths of `21` and `12`. If the parallelogram's area is `42`, what is the length of its longest diagonal?

Answer 1

`d=sqrt(585+42sqrt35)`

Explanation:

area of parallelogram is: `S=a*b*sinc`
c - angle of parallelogram
`42=21*12*sinc`
`sinc=1/6, cosc=sqrt35/6`
lengths of longest diagonal is: `d=sqrt(a^2+b^2+2abcosc`