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
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