Question

Two opposite sides of a parallelogram have lengths of `12`. If one corner of the parallelogram has an angle of `pi/4` and the parallelogram's area is `42`, how long are the other two sides?

Answer 1

`=4.95`

Explanation:

Area of the Parallelogram =
`a`x `b` x `sintheta`
where a and b are sides and θ
is the angle between them.
So we got `a=12` and `theta = pi/4`or `45^@`
We have to find out
b= ?

So we write
Area =`42`=`ab sintheta`
or
`42=12b sin45`
or
`b sin45=42/12`
or
`b sin45=7/2`
or
`b/sqrt2=7/2` since `sin45=1/sqrt2`
or
`b=7/sqrt2`
or
`b=4.95`