Step-by-step Solution:

We are given: - The area of a rhombus = \( 120 \, \text{cm}^2 \). - One diagonal = \( 24 \) cm. - We need to find the perimeter of the rhombus. Step 1: Use the Area Formula of a Rhombus The area of a rhombus is given by: \[ \text{Area} = \frac{1}{2} d_1 d_2 \] where \( d_1 \) and \( d_2 \) are the diagonals of the rhombus. Substituting the given values: \[ 120 = \frac{1}{2} \times 24 \times d_2 \] \[ 120 \times 2 = 24 \times d_2 \] \[ 240 = 24 \times d_2 \] \[ d_2 = \frac{240}{24} = 10 \text{ cm} \] Step 2: Find the Side Length of the Rhombus The diagonals of a rhombus bisect each other perpendicularly. Each half-diagonal forms a right-angled triangle with the side of the rhombus. Using the Pythagorean theorem: \[ s^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 \] Substituting \( d_1 = 24 \) and \( d_2 = 10 \): \[ s^2 = \left(\frac{24}{2}\right)^2 + \left(\frac{10}{2}\right)^2 \] \[ s^2 = 12^2 + 5^2 \] \[ s^2 = 144 + 25 \] \[ s^2 = 169 \] \[ s = \sqrt{169} = 13 \text{ cm} \] Step 3: Find the Perimeter The perimeter of a rhombus is given by: \[ \text{Perimeter} = 4s \] \[ \text{Perimeter} = 4 \times 13 = 52 \text{ cm} \] Final Answer \[ \boxed{52} \]