Question

polygon j is a scaled copy of polygon i. polygon i (purple) has a top side labeled 16, a left side labeled 24, and a bottom side labeled 8. polygon j (green) has a top side labeled 18, a left side labeled k, and a bottom side labeled 9. 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 take the bottom sides: 8 (from I) and 9 (from J)? Wait, no, wait. Wait, the top side of I is 16, top side of J is 18. Wait, or the bottom side of I is 8, bottom side of J is 9. Let's check the ratio. Let's take the bottom sides: 9/8? Wait, no, wait, maybe the top sides. Wait, 18/16? Wait, no, wait, maybe the vertical side? Wait, no, let's see. Wait, polygon I has a bottom side of 8, polygon J has a bottom side of 9. So the scale factor from I to J is 9/8? Wait, no, wait, 8 to 9: 9/8. Then the vertical side of I is 24, so the vertical side of J (k) should be 24*(9/8). Wait, let's check with the top side. Top side of I is 16, top side of J is 18. 18/16 = 9/8. Yes, that's the same. So scale factor is 9/8.

Step2: Calculate k

Now, the vertical side of I is 24, so k = 24(9/8). Let's compute that. 24 divided by 8 is 3, 39 = 27. So k = 27.

Answer:

27