Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `49`, what is the length of its longest diagonal?

Answer 1

Length of longer diagonal is `28.8 unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=49/(14*15)=0.23 :. theta=sin^-1(0.23)=13.49^0:.`

Consecutive angles are supplementary `:.theta_2=180-13.49=166.51^0`.

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+15^2-2*14*15*cos166.51) ~~28.8 unit`[Ans]