A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #16 #, what is the length of its longest diagonal?

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Answer 1 · 2018-03-04T11:13:39

Length of longer diagonal is #21.95# unit.

#s_1=14 ; s_2=8, A_p=16 ; /_theta# is one corner angle.

We know the area of the parallelogram as

#A_p=s_1*s_2*sin theta or sin theta=16/(14*8)=1/7 :.#

#theta=sin^-1(1/7)=8.21^0#.Consecutive angles are

supplementary #:.theta_2=180-8.21=171.79^0#. 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+8^2-2*14*8*cos171.79) 2~~21.95# unit

Length of longer diagonal is #21.95# unit [Ans]