A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #28 #, what is the length of its longest diagonal?

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Answer 1 · 2018-05-18T10:37:51

See below.

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We are looking for the length of diagonal:

First we need to find the length of #bbh#:

We know the area, so:

The area of a parallelogram is given as:

#"Area"="length of base"xx"height"#

#A=14h=28=>h=7#

Triangle:

#ABE# is right angled, so by Pythagoras' theorem:

#AE=sqrt(8^2-7^2)=sqrt(15)#

Triangle:

#DBE# is also right angled, so:

Length #ED=14-sqrt(15#

Using Pythagoras' theorem again:

#DB=sqrt((14-sqrt(15))^2+7^2)~~12.31082720# units squared.