A parallelogram has sides with lengths of #7 # and #15 #. If the parallelogram's area is #21 #, what is the length of its longest diagonal?

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Answer 1 · 2018-06-01T14:53:34

Length of longest diagonal #color(maroon)(d_1 = 21.9# units

Formula for length of the longest diagonal

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

as #theta# is obtuse.

#a = 15, b = 7, A_p = 21#

#A_p = a b sin theta#

#theta = arcsin (21/(15*7)) = 0.2031^c#

Length of longest diagonal #d_1 = sqrt(15^2 + 7^2 + (2 * 15 * 7 * cos (0.2031)))#

#color(maroon)(d_1 = 21.9# units