Question

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

Explanation:

Step1: Count original perimeter

Assume each grid - square side is 1 unit. Counting the side - lengths of the original polygon, if we assume the horizontal and vertical segments, say the original perimeter $P_{1}$ is 10 units (by simply adding up the lengths of all the outer - sides).

Step2: Calculate scale factor

The formula for the scale factor $k$ when comparing perimeters of similar polygons is $k=\frac{P_{2}}{P_{1}}$, where $P_{2}$ is the perimeter of the new polygon and $P_{1}$ is the perimeter of the original polygon. Given $P_{2} = 30$ units and $P_{1}=10$ units, then $k=\frac{30}{10}=3$.

Step3: Draw the scaled - copy

To draw the scaled - copy, multiply the length of each side of the original polygon by the scale factor 3. For example, if an original side has a length of 1 unit, the new side will have a length of 3 units.

Answer:

The scale factor is 3. To draw the scaled copy, multiply the length of each side of the original polygon by 3.