Question

2. If Figure X is similar to Figure Y by a scale factor k, then the perimeter of Figure Y can be found by multiplying the perimeter of figure X by ________.​

Answer 1

k

Explanation:

To understand this concept, let's consider an example. Suppose we have two similar figures, Figure X and Figure Y. If Figure X has a perimeter of 10 units and Figure Y is similar to Figure X with a scale factor of 2 (k = 2), we can find the perimeter of Figure Y by multiplying the perimeter of Figure X by the scale factor:

Perimeter of Figure Y = Perimeter of Figure X * k

Perimeter of Figure Y = 10 units * 2

Perimeter of Figure Y = 20 units

So, in this example, the perimeter of Figure Y would be 20 units.

In general, when two figures are similar, their corresponding sides are proportional. This means that the ratio of any two corresponding side lengths in Figure X and Figure Y will be equal to the scale factor k. Since the perimeter is the sum of all the side lengths, multiplying the perimeter of Figure X by the scale factor k gives us the perimeter of Figure Y.

Remember to always use the same unit of measurement for the perimeters of both figures to ensure accurate calculations.