Find the sides of the rhombus knowing that its diagonals are 1: 2 and the area of the rhombus is 12cm.

Let a rhombus absd be given, one diagonal ac = d, and the second diagonal bd = 2 * d. One of the formulas for the area of a rhombus will be as follows:

With a rhombus = ac * vd / 2 = d * 2 * d / 2 = d² = 12 cm².

Let the point of intersection of the diagonals ac and bd be the point o. Consider a triangle (rectangular) abo, which consists of legs ao and in, and the hypotenuse – the sides of the rhombus ab. We find this side as the hypotenuse along the well-known legs ao = ac / 2 = d / 2 and in = vd / 2 = 2 * d / 2 = d.

The side of the rhombus ab is determined from the equality:

(ab) ² = ao² + b² = (d / 2) ² + d² = d² / 4 + d² = 5/4 * d² = 5/4 * 12 cm² = 15 cm².

ab = √15 cm.