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A parallelogram has sides with lengths of #5 # and #9 #. If the parallelogram's area is #27 #, what is the length of its longest diagonal?

Answer 1

Claire Akin

Longest possible diagonal measures 13.3417

Given #l = 9, w = 5, Area = 27#

Area of the parallelogram = l * h = 27
#:. BE = CF = h = (Area)/l = 27 / 9= 3#

AE = DF = a = sqrt(w^2-h^2) = sqrt(5^2 - 3^2) = 4#

AF = l + a = 9 + 4 = 13#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(13 ^2 + 3^2) = 13.3417#

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Answer 2

James Atkins

The length of the longest diagonal of the parallelogram is 3√61 units.

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Answer from HIX Tutor

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