A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

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Answer 1 · 2018-01-14T06:10:01

Length of longest diagonal #AC = d_1 = color(red)(32.8596)#

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Given #a = 12, b = 21, A_p = 48#

#A_p = b * h#

#h = A_p / b = 48 / 21 = 16/7#

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#AB’ = sqrt(a^2 - h^2) = sqrt(12^2 - (16/7)^2) = 11.78#

Length of longest diagonal
#AC = d_1 = sqrt((AB + AB’)^2 + h^2) = sqrt((21+11.78)^2 + (16/7)^2#

#AC = d_1 = color(red)(32.8596)#