Question

A parallelogram has sides with lengths of `12` and `8`. If the parallelogram's area is `96`, what is the length of its longest diagonal?

Answer 1

Diagonals are of equal size: `14.42 (2dp) unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=96/(12*8)=1 :. theta=sin^-1(1)=90^0:.`.Consecutive angles are supplementary `:.theta_2=180-90=90^0`.
The angles are `90^0` each. Diagonals are of equal size.
Diagonal `=sqrt(12^2+8^2) =sqrt 208 = 14.42 (2dp) unit` [Ans]