Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `84`, what is the length of its longest diagonal?

Answer 1

`l=sqrt(421+32*sqrt21)`

Explanation:

Area of parallelogram is: `S=ab*sinA`
A - obtuse angle between sides a and b.
longest diagonal is: `l=sqrt(a^2+b^2 -abcosA)`
`cosA=-sqrt(1-sin^2A)`
`l=sqrt(a^2+b^2+ab*sqrt(1-(S/(ab))^2))`