Question

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

37.5 yards
37.5 yards

13.5 yards
13.5 yards

6 yards
6 yards

4.17 yards

Answer 1

Since the triangles \( \triangle GHJ \) and \( \triangle CDE \) are similar (\( \triangle GHJ \sim \triangle CDE \)), the ratios of the corresponding sides of the triangles are equal.

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

We need to find the length of \( DE \).

Using the side ratios of the similar triangles:

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

Substituting the known values:

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

Now, solve for \( DE \):

Cross multiply:

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

Calculate \( 9 \cdot 7.5 \):

\[
9 \cdot 7.5 = 67.5
\]

Now we have:

\[
5 \cdot DE = 67.5
\]

Divide both sides by 5 to solve for \( DE \):

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

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