Question

A parallelogram has sides with lengths of `12` and `4`. If the parallelogram's area is `12`, what is the length of its longest diagonal?

Answer 1

Longest diagonal is `15.9 unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=12/(12*4)=0.25 :. theta=sin^-1(0.25)=14.48^0:.`consecutive angles are supplementary `:.theta_2=180-14.48=165.52^0`. Longest 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(12^2+4^2-2*12*4*cos165.52) =15.9 unit` [Ans]