Which correctly completes the following statement? If the dimensions of a figure are multiplied by a scale factor of \( k \) to produce a figure that is similar to the original, then the perimeter is multiplied by and the area is multiplied by \( k^{2} \).

When the dimensions of a figure are multiplied by a scale factor \( k \) to produce a similar figure, both the perimeter and the area undergo specific changes based on the scale factor. Here's how it works: - **Perimeter:** The perimeter of a figure is a linear measurement. When each dimension is scaled by \( k \), the perimeter is also scaled by the same factor. Therefore, the perimeter is multiplied by \( k \). - **Area:** The area of a figure is a two-dimensional measurement. Scaling each dimension by \( k \) results in the area being scaled by \( k^2 \). This is because area involves two dimensions (length and width), each contributing a factor of \( k \). **Complete Statement:** >If the dimensions of a figure are multiplied by a scale factor of \( k \) to produce a figure that is similar to the original, then the perimeter is multiplied by \( k \) and the area is multiplied by \( k^{2} \). **Example:** - If you have a square with a side length of 2 units, its perimeter is \( 4 \times 2 = 8 \) units, and its area is \( 2^2 = 4 \) square units. - Scaling the square by \( k = 3 \): - New perimeter: \( 8 \times 3 = 24 \) units. - New area: \( 4 \times 3^2 = 36 \) square units. This scaling behavior holds true for all similar figures, whether they are simple shapes like squares and circles or more complex polygons. **Final Answer:** The perimeter is multiplied by \( k \) and the area is multiplied by \( k^{2} \).