A parallelogram has sides with lengths of #12 # and #5 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

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A parallelogram has sides with lengths of #12 # and #5 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

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Answer 1 · 2016-11-22T11:22:58

Length of longer diagonal is #15.96 (2dp) unit #

Explanation:

We know the area of the parallelogram as #A_p=s_1*s_2*sin theta or sin theta=42/(12*5)=0.7 :. theta=sin^-1(0.7)=44.43^0:.#consecutive angles are supplementary #:.theta_2=180-44.43=135.57^0#.

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+5^2-2*12*5*cos135.57) =15.96 (2dp) unit #[Ans]

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A parallelogram has sides with lengths of #12 # and #5 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

1 Answer

Explanation:

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