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

4.17 yards
4.17 yards

37.5 yards
37.5 yards

13.5 yards

Answer 1

To find the length of \( DE \) in triangle \( CDE \), we can use the concept of similarity since \( \triangle GHJ \sim \triangle CDE \).

Given:
- \( GH = 5 \) yards
- \( HJ = 7.5 \) yards
- \( CD = 9 \) yards

Since the triangles are similar, the ratios of their corresponding sides are equal. We can set up the ratio as follows:

\[
\frac{GH}{CD} = \frac{HJ}{DE}
\]

Now we can substitute the known values into the ratio:

\[
\frac{5}{9} = \frac{7.5}{DE}
\]

To find \( DE \), we can cross-multiply:

\[
5 \cdot DE = 9 \cdot 7.5
\]

Calculating the right side:

\[
9 \cdot 7.5 = 67.5
\]

Now the equation is:

\[
5 \cdot DE = 67.5
\]

To solve for \( DE \), divide both sides by 5:

\[
DE = \frac{67.5}{5} = 13.5 \text{ yards}
\]

Therefore, the length of \( DE \) is \( \boxed{13.5} \) yards.