Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `27`, what is the length of its longest diagonal?

Answer 1

Length of longer diagonal is `26.92 unit (2dp)`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=27/(15*12)=0.15 :. theta=sin^-1(0.15)=8.63^0:.`consecutive angles are supplementary `:.theta_2=180-8.63=171.37^0`.

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(15^2+12^2-2*15*12*cos171.37) =26.92 unit (2dp)`[Ans]