Question

A parallelogram has sides with lengths of `15` and `8`. If the parallelogram's area is `48`, what is the length of its longest diagonal?

Answer 1

The length of longer diagonal is `22.56 unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=48/(15*8)=0.4 :. theta=sin^-1(0.4)=23.58^0:.`consecutive angles are supplementary `:.theta_2=180-23.58=156.42^0`.

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(15^2+8^2-2*15*8*cos156.42) =22.56 unit`[Ans]