Question

pentagon i is a scaled copy of pentagon h. pentagon h (green) has sides labeled 16, 20, 12. pentagon i (blue) has sides labeled 12, j, 9. what is the value of j?

Explanation:

Step1: Find the scale factor

Since Pentagon I is a scaled copy of Pentagon H, the ratio of corresponding sides is equal. We can find the scale factor using the bottom sides: $\frac{9}{12}=\frac{3}{4}$.

Step2: Apply the scale factor to find j

The side of length 20 in Pentagon H corresponds to side j in Pentagon I. So we multiply 20 by the scale factor: $j = 20\times\frac{3}{4}$.

Step3: Calculate the value of j

$20\times\frac{3}{4}=\frac{60}{4} = 15$.

Answer:

15