Question

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?

Answer 1

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`