Question

a nonagon has a perimeter of 28 meters. if the nonagon is dilated with a scale factor of \\(\frac{10}{7}\\), what is the perimeter of its image?

Explanation:

Step1: Recall dilation of perimeter

When a figure is dilated by a scale factor \( k \), the perimeter of the image is the original perimeter multiplied by \( k \).

Step2: Apply the scale factor to perimeter

Original perimeter \( P = 28 \) meters, scale factor \( k=\frac{10}{7} \). So the new perimeter \( P'=P\times k = 28\times\frac{10}{7}\).
Simplify \( 28\times\frac{10}{7}=\frac{28\times10}{7}=4\times10 = 40 \).

Answer:

The perimeter of its image is 40 meters.