Question

Two opposite sides of a parallelogram each have a length of `1`. If one corner of the parallelogram has an angle of `(3 pi)/4` and the parallelogram's area is `24`, how long are the other two sides?

Answer 1

The other sides have a length of (approximately) `33.94` units

Explanation:

If you are getting a lot of these types of questions, it is useful to know that for a parallelogram with sides of length `L` and `W` and an interior angle of `theta`
`color(white)("XXX")"Area" = sin(theta) * L * W`

In this case using `theta=(3pi)/4` and `W=1` we have
`color(white)("XXX")24=sin((3pi)/4) * L * 1`

`color(white)("XXXX")=1/sqrt(2)L`

`color(white)("XXX")rarr L = 24sqrt(2)~~33.94`