The diagonals of the rectangle intersect at an angle of 60 degrees. The length of the diagonal is 12.

The diagonals of the rectangle intersect at an angle of 60 degrees. The length of the diagonal is 12. Find the length of the larger side of the rectangle.

Crossing, the diagonals form a triangle with the smaller side of the rectangle. This is an isosceles triangle, because the diagonals are halved in the rectangle.

Let us determine what the angles at the base (smaller side) will be equal to when the angle between the diagonals is 60 °:

(180 – 60): 2 = 60.

That is, all three angles are 60 °. Then the smaller side is equal to half the diagonal:

12: 2 = 6.

Let’s find out what the area of the rectangle will be:

1/2 * 12 ^ 2 * √3 / 2 = 36√3.

Let’s find out the length of the longer side:

36√3: 6 = 6√3.

Answer: 6√3.