Question

A parallelogram has sides with lengths of `9` and `8`. If the parallelogram's area is `56`, what is the length of its longest diagonal?

Answer 1

The length of longer diagonal is `15.35 unit`

Explanation:

We know, the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=56/(9*8)=0.78 :. theta=sin^-1(0.78)=51.06^0:.`.Consecutive angles are supplementary `:.theta_2=180-51.06=128.94^0`.

Longer diagonal can be found by applying cosine law:`d_l= sqrt(s_1^2+s_2^2-2*s_1*s_2*costheta_2)=sqrt(9^2+8^2-2*9*8*cos128.94) =15.35 unit`[Ans]