Find the side of the rhombus if its area is 12, and the lengths of the diagonals are 1: 2.

1. The tops of the rhombus – A, B, C, D. The area of the rhombus S = 12 units. ВD: AC = 1: 2.
2. AC = 2ВD.
3.S = AC x ВD / 2. We replace the speaker with 2ВD:
2ВD x ВD / 2 = 12 units of measurement².
ВD² = 12 units of measurement².
ВD = √12 = 2√3 units.
AC = 2ВD = 2 x 2√3 = 4√3 units.
4. Considering that the diagonals are perpendicular and the intersection point is divided in half,
calculate the length of the rhombus side:
AD = √ (AC / 2) ² + (ВD / 2) ² = √ (4√3 / 2) ² + (2√3 / 2) ² = √4 x 3 + 3 = √15 units.