Question

A parallelogram has sides with lengths of `16` and `9`. If the parallelogram's area is `64`, what is the length of its longest diagonal?

Answer 1

Longer diagonal is `24.39` unit.

Explanation:

We know the area of the parallelogram as `A_p=s_1*s_2*sin theta or sin theta=64/(16*9)=0.444 :. theta=sin^-1(0.444)=26.39^0:.`consecutive angles are supplementary `:.theta_2=180-26.39=153.61^0`.

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+9^2-2*16*9*cos153.61) =24.39` unit [Ans]