Question

Two opposite sides of a parallelogram have lengths of `3`. If one corner of the parallelogram has an angle of `pi/4` and the parallelogram's area is `36`, how long are the other two sides?

Answer 1

Other two parallel sides are `color(green)(12sqrt2` long each.

Explanation:

Area of parallelogram `A_p = b h = b a sin theta` as `h = a sin theta`

Given : `b = 3, A_p = 36, theta = pi/4`

To find a.

`a = A_p / (b sin theta) = cancel(36)^color(brown)(12) / (cancel(3 ) sin (pi /4) )= 12 / (1/sqrt2) = 12 sqrt2`