Question

pentagon k is a scaled copy of pentagon j.
diagram of pentagon j (top side 20, left side 40, bottom side 24) and pentagon k (top side 15, left side 30, bottom side 18)
what scale factor takes pentagon j to pentagon k?
text box
submit
work it out
not feeling ready yet? these can help:
solve one-step multiplication and division equations with decimals ...
add, subtract, multiply, or di

Explanation:

Step1: Recall scale factor formula

The scale factor from figure \( J \) to figure \( K \) is the ratio of a corresponding side length of \( K \) to the corresponding side length of \( J \). Let's take the top sides: length of \( J \) is \( 20 \), length of \( K \) is \( 15 \).

Step2: Calculate the scale factor

Scale factor \( = \frac{\text{Length of } K}{\text{Length of } J} = \frac{15}{20} \)
Simplify \( \frac{15}{20} = \frac{3}{4} = 0.75 \) (we can also check with other sides: \( \frac{30}{40}=\frac{3}{4} \), \( \frac{18}{24}=\frac{3}{4} \), so it's consistent).

Answer:

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