Area of a rhombus is 24 . If one of its diagonals is 6 cm then its perimeter is ________ cm.

The area of a rhombus is given by the formula: Area = 1/2 * d1 * d2, where d1 and d2 are the lengths of the diagonals.

Given that the area is 24 cm² and one of the diagonals (d1) is 6 cm, we can substitute these values into the formula to find the length of the other diagonal (d2):

24 = 1/2 * 6 * d2 24 = 3 * d2 d2 = 24 / 3 d2 = 8 cm

The diagonals of a rhombus bisect each other at right angles. Therefore, each side of the rhombus is the hypotenuse of a right-angled triangle with sides of lengths 1/2 * d1 and 1/2 * d2.

We can use the Pythagorean theorem to find the length of each side (s):

s = sqrt[(1/2 * d1)² + (1/2 * d2)²] s = sqrt[(1/2 * 6)² + (1/2 * 8)²] s = sqrt[9 + 16] s = sqrt[25] s = 5 cm

The perimeter of a rhombus is given by the formula: Perimeter = 4 * s. Substituting the value of s we found:

Perimeter = 4 * 5 Perimeter = 20 cm

So, the perimeter of the rhombus is 20 cm.