Question

pentagon k is a scaled copy of pentagon j.
diagrams: pentagon j with side lengths 20, 40, 24; pentagon k with side lengths 15, 30, 18
what scale factor takes pentagon j to pentagon k?

Explanation:

Step1: Recall scale factor formula

The scale factor from a figure to its scaled copy is the ratio of a length in the copy to the corresponding length in the original. So, scale factor \( = \frac{\text{Length in } K}{\text{Length in } J} \).

Step2: Choose corresponding sides

Let's take the top sides: length in \( J \) is 20, length in \( K \) is 15. Or the vertical sides: 40 in \( J \), 30 in \( K \). Or the bottom sides: 24 in \( J \), 18 in \( K \). Let's use the top sides.

Step3: Calculate the ratio

Using top sides: \( \frac{15}{20} = \frac{3}{4} \). Let's check with vertical sides: \( \frac{30}{40} = \frac{3}{4} \). Bottom sides: \( \frac{18}{24} = \frac{3}{4} \). So the scale factor is \( \frac{3}{4} \) or 0.75.

Answer:

\(\frac{3}{4}\) (or 0.75)