A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?

1 Answer
Cesareo R.
May 16, 2016

The longest diagonal #=20.203 #

Explanation:

The parallelogram with sides #a,b# has an area computed as
#A = a times b times sin(theta) = 84#
Solving for #theta# we obtain #theta_0 = 2.29353#[rad]
Associating now an oriented segment to each side we get
#vec a = a{cos(theta_0),sin(theta_0)}, vec b = b{1,0}#
The two diagonals are obtained as
#vec d_1 = vec a + vec b#
#vec d_2 = vec a - vec b#
Computing their length we get
#norm(vec d_1) = 10.5753#
#norm(vec d_2) = 20.203#

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