A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

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Answer 1 · 2018-05-22T10:30:16

Longest diagonal #color(blue)(d_1 = 16.55)# units

Length of longest diagonal is given by

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

Where a and b are the two pairs of parallel lines and #theta# the acute angle between non parallel sides

To find #theta# first.

#Area # #A_p = a b sin theta#

Given #a = 9, b = 8, A_p = 32#

#sin theta=32 / (9 * 8) = 4/9#

#theta = sin ^-1 (4/9) = 0.4606#

#Longest diagonal #d_1 = sqrt(9^2 + 8^2 + (2 * 9 * 8 * cos 0.4606))#

#color(blue)(d_1 = 16.55# units