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Let's go through each of the problems step by step.

### Problem 5
We have two similar triangles, \( \triangle JKL \sim \triangle GKH \), and we need to solve for \( x \).

Since these triangles are similar, we can set up a proportion between the corresponding sides.

#### Step 1: Identify corresponding sides
1. \( JK \) in \( \triangle JKL \) corresponds to \( GK \) in \( \triangle GKH \).
2. \( JL \) in \( \triangle JKL \) corresponds to \( GH \) in \( \triangle GKH \).
3. \( KL \) in \( \triangle JKL \) corresponds to \( KH \) in \( \triangle GKH \).

#### Step 2: Set up the proportion
The side lengths are given as follows:
- \( JK = 6 \), \( GK = 4 \), and \( JL = 15 \).
  
Using the ratio \( \frac{JL}{GH} = \frac{JK}{GK} \):
\[
\frac{15}{x} = \frac{6}{4}
\]

#### Step 3: Solve for \( x \)
1. Cross-multiply to find \( x \):
   \[
   6x = 15 \times 4
   \]
2. Simplify:
   \[
   6x = 60
   \]
3. Divide by 6:
   \[
   x = 10
   \]

So, \( x = 10 \) for Problem 5.

### Problem 6
We are given two similar triangles, \( \triangle ABC \sim \triangle ADE \), and we need to solve for \( x \) and \( y \).

#### Step 1: Identify the proportions between corresponding sides
Since the triangles are similar, corresponding sides are proportional:
1. \( \frac{AB}{AD} = \frac{BC}{DE} = \frac{AC}{AE} \).

From the diagram:
- \( AB = 3 \), \( AC = 4 \), and \( AD = y \).
- \( BC = 5 \) and \( DE = 12.5 \).

#### Step 2: Set up proportions for \( x \)
Since \( \frac{AC}{AE} = \frac{AB}{AD} \), we get:
\[
\frac{4}{x} = \frac{3}{y}
\]



We are given two similar triangles, ΔJKL ∼ ΔGKH and ΔABC ∼ ΔADE, and we need to solve for x and y in the triangles. Show your work.

Learn how to solve for x and y in similar triangles ΔJKL ∼ ΔGKH and ΔABC ∼ ΔADE by setting up proportions and using the triangle similarity theorem. Suitable for students in Grades 9-10, this problem covers key concepts in geometry.

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