# The diagonal difference between the rhombus is 10 cm, and its area is 220 cm2. Find the perimeter of the rhombus.

Let x denote the length of the smaller diagonal of the given rhombus.

Since the difference between the diagonals of the rhombus is 10 cm, the length of the larger diagonal of this rhombus should be equal to x + 10 cm.

According to the condition of the problem, the area of this rhombus is 220 cm ^ 2.

Since the area of any rhombus is half the product of its diagonals, we can compose the following equation:

x * (x + 10) / 2 = 220,

solving which, we get:

x * (x + 10) = 220 * 2;

x * (x + 10) = 440;

x ^ 2 + 10x = 440;

x ^ 2 + 10x – 440 = 0;

x = -5 ± √ (25 + 440) = -5 ± √465;

x = -5 + √465.

Find the 2nd diagonal:

x + 10 = -5 + √465 + 10 = √465 + 5.

We find the length of the side of the rhombus:

√ ((√465 – 5) ^ 2 + (√465 + 5) ^ 2) / 2 = √ (465 + 25 + 465 + 25) / 2 = √980 / 2 = √245 = 7√5.

Therefore, the perimeter of the rhombus is 4 * 7√5 = 28√5 cm.

Answer: the perimeter of the rhombus is 28√5 cm.