Question

A parallelogram has sides with lengths of `12` and `5`. If the parallelogram's area is `42`, what is the length of its longest diagonal?

Answer 1

Length of longer diagonal is `15.96 (2dp) unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=42/(12*5)=0.7 :. theta=sin^-1(0.7)=44.43^0:.`consecutive angles are supplementary `:.theta_2=180-44.43=135.57^0`.

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(12^2+5^2-2*12*5*cos135.57) =15.96 (2dp) unit`[Ans]