A parallelogram has sides with lengths of #14 # and #6 #. If the parallelogram's area is #77 #, what is the length of its longest diagonal?

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Answer 1 · 2018-02-14T12:01:33

Longer diagonal is #17.3 # unit

#A_p=77 , s_1=14 ,s_2=6#

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

# sin theta=77/(14*6)~~0.917 :. theta=sin^-1(0.917)~~66.44^0#

Consecutive angles are supplementary

#:.theta_2=180-66.44=113.56^0#. 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(14^2+6^2-2*14*6*cos113.56) =17.3# unit

Longer diagonal is #17.3 # unit [Ans]

[Ans}