# The perimeter of the rhombus is 68, the area of the rhombus is 240. Find the diagonals of the rhombus.

Since the lengths of the sides of the rhombus are equal, then AB = BC = CD = AD = Ravsd / 4 = 68/4 = 17 cm.

Let the length of the smaller diagonal be 2 * X cm, and the length of the larger diagonal is 2 * Y cm.

Then OB = 2 * X / 2 = X cm, AO = 2 * Y / 2 = Y cm.

The area of ​​the rhombus is equal to: Savsd = AC * BD / 2 = 2 * Y * 2 * X / 2.

2 * X * Y = 240.

X * Y = 120. (1)

In a right-angled triangle AOB, according to the Pythagorean theorem:

AB ^ 2 = AO ^ 2 + OB ^ 2.

289 = Y ^ 2 + X ^ 2. (2).

Let’s solve the system of equations 1 and 2.

Y = 120 / H.

289 = (120 / X) ^ 2 + X ^ 2.

289 * X ^ 2 = 14,400 + X ^ 4.

X ^ 4 – 289 * X ^ 2 + 14,400 = 0.

Let X ^ 2 = Z, then Z ^ 2 – 289 * Z + 14400 = 0.

Z1 = 64, Z2 = 225.

X1 = 8 cm, X2 = 15 cm.

Y1 = 120/8 = 15 cm.

Y2 = 120/15 = 8 cm

Then, if BD = 2 * 8 = 16 cm, AC = 2 * 15 = 30 cm.

If BD = 2 * 15 = 30 cm, AC = 2 * 8 = 16 cm.

Answer: The diagonals of the rhombus are 16 cm and 30 cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.