A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #96 #, what is the length of its longest diagonal?

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Answer 1 · 2016-09-18T03:47:57

#sqrt433=20.81#

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ABCD is the parallelogram.

Parallelogram area #A_P = bxxh#
where b=base, h=height

Given #A_P=96# and #b=8 => h=96/8=12#

Note that triangle CDE is a right-angled triangle :
#=> x=sqrt(15^2-12^2) = sqrt81=9#

Again, note that triangle CAE is also a right-angled triangle:

#AC# = the longer diagonal of the parallelogram ABCD

#=> AC=sqrt((8+9)^2+12^2) =sqrt(17^2+12^2) =sqrt433 =20.81#