Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `150`, what is the length of its longest diagonal?

Answer 1

`=23.8`

Explanation:

Area of Parallelogram `=150=ab sintheta` where `a=15` and `b=12`
or
`150=15times12timessintheta`
or

`sin theta=150/12times1/15`
or
`sin theta=5/6`
or
`theta=sin^-1(5/6)`
or
`theta=56.44`

To find the longer diagonal `=y=?`

we have to get the supplementary of the angle `56.44`

So we have Angle `180-56.44=123.56`

Using the Law of Cosine we can write
`y^2=15^2+12^2-2times15times12cos(123.56)`
`=225+144-2times15times12(-0.55)`
`=369+198`
`=567`
or
`y=sqrt567`
`=23.8`