Question

A parallelogram has sides with lengths of `5` and `9`. If the parallelogram's area is `9`, what is the length of its longest diagonal?

Answer 1

`13.94` unit

Explanation:

The area of parallelogram `= b*c*sin theta`, where `theta` is an angle between sides `b and c`
Therefore,

`5*9*sin theta=9`
`sin theta=9/45=1/5`

`theta=11.54^0 and 168.46^0`

The longest diagonal is the length facing to the highest angle.
Let say it length is `=a` and use formula `a^2=b^2+c^2-2*b*c*kos theta`

`a^2=5^2+9^2-2*5*9*cos 168.46^0`

`a^2=25+81-90*(-0.98)`
`a^2=106+88.2`
`a^2=194.20`
`a=13.94`