Question

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

6 yards
6 yards

37.5 yards
37.5 yards

13.5 yards
13.5 yards

4.17 yards

Answer 1

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**.