Question

△GHJ∼△CDE
. GH=5
yards, HJ=7.5
yards, CD=9
yards. What is the length of DE¯¯¯¯¯¯¯¯
? (1 point)
Responses

13.5 yards
13.5 yards

37.5 yards
37.5 yards

4.17 yards
4.17 yards

6 yards

Answer 1

Since triangles \( \triangle GHJ \) and \( \triangle CDE \) are similar (denoted by \( \triangle GHJ \sim \triangle CDE \)), the lengths of their corresponding sides are in proportion.

The sides are:
- \( GH \) corresponds to \( CD \)
- \( HJ \) corresponds to \( DE \)

From the problem, we have:
- \( GH = 5 \) yards
- \( HJ = 7.5 \) yards
- \( CD = 9 \) yards

To find the length of \( DE \), we can set up a proportion based on the corresponding sides:
\[
\frac{GH}{CD} = \frac{HJ}{DE}
\]
Substituting the known values:
\[
\frac{5}{9} = \frac{7.5}{DE}
\]
Now, 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:
\[
DE = \frac{67.5}{5} = 13.5
\]
Thus, the length of \( DE \) is **13.5 yards**.