A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #96 #, what is the length of its longest diagonal?

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Dec 10, 2017

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Length of the longest diagonal AC is 32.3109

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Given #l = 24, w = 9, Area = 96#

Area of the parallelogram = l * h = 96
#:. BE = CF = h = (Area)/l = 96 / 24 = 4#

AE = DF = a = sqrt(w^2-h^2) = sqrt(9^2 - 4^2) = 8.0623#

AF = l + a = 24 + 8.0623 = 32.0623#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(32.0623^2 + 4^2) = 32.3109#

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