Question

polygon j is a scaled copy of polygon i. what is the value of k?

Explanation:

Step1: Find the scale factor

Since polygon J is a scaled - copy of polygon I, we can find the scale factor by comparing corresponding sides. Let's use the pair of horizontal sides. The length of the horizontal side in polygon I is 16 and in polygon J is 18. The scale factor $s=\frac{18}{16}=\frac{9}{8}$.

Step2: Calculate the value of k

We know that the corresponding side to side k in polygon I has a length of 24. To find k, we multiply the length of the corresponding side in polygon I by the scale factor. So $k = 24\times\frac{9}{8}$.
$k=\frac{24\times9}{8}=\frac{216}{8}=27$.

Answer:

27