A parallelogram has sides with lengths of #6 # and #16 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

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Answer 1 · 2018-03-27T11:49:28

Length of longer diagonal is #21.75# unit.

#s_1=6 , s_2=16 , A_p=32#

We know the area of the parallelogram as

#A_p=s_1*s_2*sin theta or sin theta=32/(6*16)=1/3 :.#

#theta=sin^-1(1/3)=19.47^0#.Consecutive angles are

supplementary #:.theta_2=180-19.47=160.53^0#

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(6^2+16^2-2*6*16*cos160.53) ~~21.75# unit

Length of longer diagonal is #21.75# unit [Ans]