Question

draw a scaled copy of this polygon that has a perimeter of 30 units. what is the scale factor? explain how you know.

Explanation:

Since the original perimeter of the polygon is not given, we'll assume the original perimeter is \(P_{1}\) and the new perimeter is \(P_{2} = 30\) units. The scale - factor \(k\) for perimeters of similar polygons is given by the ratio of the perimeters of the new and the original polygons.

Step1: Recall the scale - factor formula for perimeters

The formula for the scale - factor \(k\) between two similar polygons in terms of perimeters is \(k=\frac{P_{2}}{P_{1}}\), where \(P_{2}\) is the perimeter of the scaled - copy and \(P_{1}\) is the perimeter of the original polygon.

Step2: Assume an original perimeter value (for illustration purposes)

Let's assume the original perimeter \(P_{1}=10\) units. Then, using the formula \(k = \frac{P_{2}}{P_{1}}\), we substitute \(P_{2}=30\) and \(P_{1}=10\).
\[k=\frac{30}{10}=3\]

To draw the scaled - copy:

1. Measure the length of each side of the original polygon.
2. Multiply the length of each side of the original polygon by the scale - factor \(k\). For example, if a side of the original polygon has length \(s_{1}\), the length of the corresponding side of the scaled - copy \(s_{2}=k\times s_{1}\).
3. Use a ruler and a protractor (if needed for angles) to draw the new polygon with the new side - lengths.

Answer:

If the original perimeter is \(10\) units, the scale - factor is \(3\). In general, the scale - factor \(k=\frac{30}{P_{1}}\), where \(P_{1}\) is the perimeter of the original polygon.