Question

A parallelogram has sides with lengths of `16` and `15`. If the parallelogram's area is `75`, what is the length of its longest diagonal?

Answer 1

Length of longer diagonal is `30.61(2dp) unit`

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=75/(16*15)=0.3125 :. theta=sin^-1(0.3125)=18.21^0`.

Consecutive angles are supplementary `:.theta_2=180-18.21=161.79^0`.

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(16^2+15^2-2*16*15*cos161.79) =30.61(2dp) unit`[Ans]