Given that △GHJ is similar to △CDE (denoted as △GHJ ∼ △CDE), we can use the properties of similar triangles to determine the length of DE.
The sides of similar triangles are proportional. This means we have:
\[ \frac{GH}{CD} = \frac{HJ}{DE} \]
From the information provided:
- \(GH = 5\) yards
- \(HJ = 7.5\) yards
- \(CD = 9\) yards
- \(DE\) is what we want to find.
We can set up the proportion as follows:
\[ \frac{5}{9} = \frac{7.5}{DE} \]
Now, we cross-multiply to solve for \(DE\):
\[ 5 \cdot DE = 7.5 \cdot 9 \]
Calculating the right side:
\[ 5 \cdot DE = 67.5 \]
Now, divide both sides by 5:
\[ DE = \frac{67.5}{5} = 13.5 \text{ yards} \]
Thus, the length of \(DE\) is 13.5 yards.