A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?

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Answer 1 · 2018-04-28T10:21:57

#color(green)("length of Longest diagonal " bar(AC) = 19.97#

#"Given : " AB = b = 12, AD = a = 8, Area = 12, " To find " AC = q#

#bar(EC) = h = (Area) / b = 12 / 12 = 1#

#bar(BE) = sqrt((BC)^2 - (CE)^2) = sqrt(a^2 - h^2)#

#bar(BE) = sqrt(8^2 - 1^2) = 7.94#

#bar(AE) = AB + BE = 12 + 7.94 = 19.94#

#bar(AC) = sqrt((AE)^2 + (EC)^2) = sqrt(19.94^2 + 1^2) = 19.97#

#color(green)("length of Longest diagonal " bar(AC) = 19.97#