Question

A parallelogram has sides with lengths of `14` and `12`. If the parallelogram's area is `70`, what is the length of its longest diagonal?

Answer 1

The length of longer diagonal is `25.41 unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=70/(14*12)=0.416 :. theta=sin^-1(0.416)=24.62^0:.`consecutive angles are supplementary `:.theta_2=180-24.62=155.38^0`.

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(14^2+12^2-2*14*12*cos155.38) =25.41 unit`[Ans]