Question

The lengths of two adjacent sides of a parallelogram are 6 and 14. If the measure of an included angle is 60, find the length of the shorter diagonal of the parallelogram.

Answer 1

Let the name of the parallelogram be ABCD, the two adjacent sides of the parallelogram be AB and AD. AB=14 and AD= 6. The shorter diagonal of parallelogram is BD. The angle between AB and AD is 60.

In triangle ABD, according to the cosine rule,

BD^2=AB^2+AD^2-2(AB)*(AD) cos(60)

= 14^2+6^2-(2)14)(6)(0.5)

=196+36-84

= 232-84

=148

BD^2=148

BD=12.1655

So the length of the shorter diagonal is 12.1655 unit.