A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

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Answer 1 · 2018-06-01T13:12:48

Longest diagonal #d_1 = 26.82# units

#a = 15, b = 12, A_p = 42#

Applying Law of cosines,

Longest diagonal #d_1 = sqrt(a^2 + b^2 + (2 a b cos theta)# as #theta# is obtuse.

Area of parallelogram #A_p = a b sin theta#

#theta = sin ^-1 (A_p / ( a * b))#

#theta = sin ^-1 (42 / (15 * 12) ) = 0.2355^c#

#d_1 = sqrt(a^2 + b^2 + (2 a b cos theta))#

#d_1 = sqrt(15^2 + 12^2 + (2 * 15 * 12 * cos (0.2355))#

Longest diagonal #d_1 = 26.82# units