The area of the rhombus is 120, and one of the diagonals is larger than the other by 14. Find the diagonals of the rhombus.

It is known from the condition that the area of ​​the rhombus is 120, and one of the diagonals is larger than the other by 14.

In order to find the length of the diagonals of the rhombus, we introduce the variable x, we denote it one of the diagonals, then the second can be written as (x + 14).

Recall the formula for finding the area of ​​a rhombus through the diagonals:

S = 1/2 * d1 * d2. where d1 and d2 are the lengths of the diagonals of the rhombus.

Substitute the known values ​​and solve the resulting equation:

120 = 1/2 * x * (x + 14);

x ^ 2 + 14x – 240 = 0;

We solve the resulting equation:

D = 1156;

x1 = 10; x2 = -24.

The second root does not fit.

So, one of the diagonals is 10, and the other is 10 + 14 = 28.

Answer: 10; 28.