A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #4 #, what is the length of its longest diagonal?

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Answer 1 · 2018-01-09T11:55:33

The length of longer diagonal is #20.0# unit.

The area of the parallelogram as #A_p=s_1*s_2*sin theta# or

#A_p=4,s_1=12 , s_2=8 :.sin theta=4/(12*8)=0.0416#

#:. theta=sin^-1(0.0416)~~2.39^0 # Consecutive angles are

supplementary #:.theta_2=180-2.39=177.61^0#.

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(12^2+8^2-2*12*8*cos177.61) ~~20.0# unit

The length of longer diagonal is #20.0# unit [Ans]