The diagonals of the parallelogram are 6 and 8, and the angle between them is 60 degrees.

The diagonals of the parallelogram are 6 and 8, and the angle between them is 60 degrees. Find the perimeter of the parallelogram.

The diagonals of the parallelogram form two pairs of equal triangles, since they are divided in half by the point of their intersection.

We get the first pair of triangles, where there are two sides of 3 and 4 cm and an angle between them of 60 °. By the cosine theorem:

x ^ 2 = 3 ^ 2 + 4 ^ 2 – 2 * 3 * 4 * cos 60 °;

x ^ 2 = 25 – 12;

x ^ 2 = 13;

x = 13 ^ (1/2) cm.

In the second pair of triangles, there will be an angle of 120 ° between the same sides:

y ^ 2 = 3 ^ 2 + 4 ^ 2 – 2 * 3 * 4 * cos 120 °;

y ^ 2 = 25 + 24 * 1/2;

y = 37 ^ (1/2) cm;

P = (2 * 13 ^ (1/2) + 2 * 37 ^ (1/2)) see.