# The side of the rhombus refers to one of its diagonals as 5: 6. The second diagonal is exactly 40 cm.

The side of the rhombus refers to one of its diagonals as 5: 6. The second diagonal is exactly 40 cm. Find the perimeter of the rhombus.

By condition, BC / BD = 5/6.

Let the sides of the rhombus be 5 * X, then the smaller diagonal will be 6 * X.

Consider a right-angled triangle BOC, leg BO = 6 * X / 2 = 3 * X, leg OC = AC / 2 = 40/2 = 20 cm, hypotenuse BC = 5 * X.

Then, by the Pythagorean theorem, BC ^ 2 = BO ^ 2 + OC ^ 2.

(5 * X) ^ 2 = (3 * X) ^ 2 + 15 ^ 2.

25 * X ^ 2 – 9 * X ^ 2 = 400.

16 * X ^ 2 = 400.

X ^ 2 = 25.

X = 5.

Then BC = AB = AD = CD = 5 * 5 = 25 cm.

Ravsd = 4 * 25 = 100 cm.

Answer The perimeter of the rhombus is 100 cm.

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