A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #45 #, what is the length of its longest diagonal?

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Answer 1 · 2018-01-09T15:33:28

Longest diagonal #d_1 = color(blue)(15.5224)#

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Area of parallelogram
#A_p = l * h = l * w * sin theta#

#w sin theta = A_p / l = 45 / 12#

#sin theta = 45 / (12 * 8) = 0.4688#

#theta = sin ^(-1) (0.4688) = 0.4879^c#

#theta / 2 = 0.4879 / 2 = 0.244^c#

Longest diagonal #d_1 = h / sin (theta / 2)#

#d_1 =( w sin theta) / sin (theta / 2)#

#d_1 = (45 /12) / sin (0.244) = 15.5224#