Question

A parallelogram has sides with lengths of `15` and `8`. If the parallelogram's area is `90`, what is the length of its longest diagonal?

Answer 1

Longer diagonal is `21.16` unit.

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=90/(15*8)=0.75 :. theta=sin^-1(0.75)=48.59^0:.`consecutive angles are supplementary `:.theta_2=180-48.59=131.41^0`. 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+8^2-2*15*8*cos131.41) =21.16 unit`[Ans]