Question

A parallelogram has sides with lengths of `14` and `9`. If the parallelogram's area is `56`, what is the length of its longest diagonal?

Answer 1

`=22.45`

Explanation:

Area of Parallelogram `=56=ab sintheta` where `a=14` and `b=9`
or
`56=14times9timessintheta`
or

`sin theta=56/14times1/9`
or
`sin theta=4/9`
or
`theta=sin^-1(4/9)`
or
`theta=26.4`

To find the longer diagonal `=y=?`

we have to get the supplementary of the angle `26.4`

So we have Angle `180-26.4=153.6`

Using the Law of Cosine we can write
`y^2=14^2+9^2-2times14times9cos(153.6)`
`=196+81-2times14times9(-0.9)`
`=196+81+226.8`
`=504`
or
`y=sqrt504`
`=22.45`