A parallelogram has sides with lengths of #18 # and #4 #. If the parallelogram's area is #27 #, what is the length of its longest diagonal?

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Answer 1 · 2018-05-22T04:06:16

Measure of longest diagonal #color(purple)(d_1 = 21.76#

Area of parallelogram #A = a b sin theta#

Given : #A = 27, a = 18, b = 4#

To find the measure of longest diagonal.

#18 * 4 * sin theta = 27#

#sin theta = 27 / (18 * 4) = 3/8#

#theta = sin ^-1 (3/8) = 0.3844^c#

Longest diagonal is given by the formula

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

#d_1 = sqrt(18^2 + 4^2 + (2 * 18 * 4 * cos 0.3844))#

Longest diagonal #d_1 = 21.76#