The length of a rectangle is twice its width. If the perimeter of the rectangle is 30 cm , find its area. \( \left\lfloor\mathrm{cm}^{2}\right. \)

Let the width be \( w \) and the length be \( 2w \). 1. The perimeter \( P \) of a rectangle is given by: \[ P = 2(w + 2w) = 2(3w) = 6w. \] 2. Given that the perimeter is \( 30 \) cm, set up the equation: \[ 6w = 30. \] 3. Solve for \( w \): \[ w = \frac{30}{6} = 5 \text{ cm}. \] 4. Find the length: \[ \text{Length} = 2w = 2 \times 5 = 10 \text{ cm}. \] 5. Calculate the area \( A \) of the rectangle: \[ A = \text{width} \times \text{length} = 5 \times 10 = 50 \text{ cm}^2. \] Thus, the area of the rectangle is \( 50 \text{ cm}^2 \).