Question

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

Answer 1

Longer diagonal is `22.96` unit.

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=15/(15*8)=0.125 :. theta=sin^-1(0.125)=7.18^0:.`.Consecutive angles are supplementary `:.theta_2=180-7.18=172.82^0`.

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(15^2+8^2-2*15*8*cos172.82) =22.96` unit[Ans]