The diagonals of the rhombus are in a ratio of 3: 5. Find the length of the larger diagonal if the area of the rhombus is 120.

Let’s denote the diagonals of the rhombus as D and d.
According to the conditions of the problem D: d = 3: 5, therefore D = 3 / 5d.
The area of the rhombus is: S = 1 / 2D * d.
Substitute D into this formula and get: S = 1 / 2d * 3 / 5d = 3 / 10d ^ 2.
By hypothesis, S = 120, which means:
120 = 3 / 10d ^ 2,
120 * 10/3 = d ^ 2,
d ^ 2 = 400,
d = 20, therefore D = 3/5 * 20 = 12.
Answer: the length of the larger diagonal is d = 20.