A parallelogram has sides with lengths of #16 # and #6 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

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Answer 1 · 2016-12-27T17:37:48

#2 sqrt 73#

/_/ ABCD

#|AB| = 16, |BC| = 6 \Rightarrow |CD| = 16, |DA| = 6#

#sin#  #angle DAB = |DH| / |DA| = h / 6#, DH perpendicular to AB

Area = #1/2 * |AB| * h = 1/2 * 16 * 6 * sin angle DAB = 48#

#sin angle DAB = 48/(8*6) \Rightarrow Â = 90º#

Rectangle. Pythagora.

#|AC| = |BD| = x, 16^2 + 6^2 = x^2 = 256 + 36 = 292#

#x = sqrt 292#