Find the diagonals of the rhombus, considering that one of them is 5/6 of the other, and the area

Find the diagonals of the rhombus, considering that one of them is 5/6 of the other, and the area of the rhombus is 540 cm * 2.

The area of ​​a rhombus can be found through its diagonals using the following formula:

S = 1 / 2d1d2, where d1 and d2 are the diagonals of the rhombus.

It is known from the conditions of the problem that one of the diagonals of the rhombus is equal to 5/6 of the second diagonal. That is, let’s say:

d1 = 5 / 6d2.

We also know the area of ​​the rhombus. Hence, we can form the following equation:

½ * 5 / 6d2 * d2 = 540.

Let’s solve the resulting equation:

½ * 5 / 6d2 * d2 = 540,

5/12 * d2² = 540,

d2² = 540 / 5/12,

d2² = 540 * 12/5,

d2² = 1296,

d2 = ± √1296,

d2 = ± 36.

Since the diagonal can only be a positive value, then d2 = 36 cm. We find d1:

d1 = 5/6 * 36 = 5 * 6 = 30 cm.

Answer: the diagonals of the rhombus are 30 cm and 36 cm.