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The image you've uploaded shows a problem involving similar triangles, where you need to determine how many times larger the area of one triangle is compared to another.

### Problem Explanation:
The triangles are scaled copies of each other, meaning they are similar triangles. When two triangles are similar, their corresponding side lengths are proportional, and the ratio of their areas is the square of the ratio of their corresponding sides.

### Given Triangles:
1. **Triangle F:** Base = 6, Height = 10
2. **Triangle G:** Base = 3, Height = 5
3. **Triangle H:** Base = 1.5, Height = 2.5

### Question:
You are asked to compare the area of the second triangle in each pair with the area of the first triangle and determine how many times larger the area of the second triangle is.

### Steps to Solve:
1. **Find the Area of Each Triangle:**
   - Area of a triangle = \( \frac{1}{2} \times \text{Base} \times \text{Height} \).

2. **Compare the Areas:**
   - Since the triangles are similar, the ratio of the areas will be the square of the ratio of their corresponding sides.

### Calculations:

1. **Triangle F**:
   - Area = \( \frac{1}{2} \times 6 \times 10 = 30 \) square units.
   
2. **Triangle G**:
   - Area = \( \frac{1}{2} \times 3 \times 5 = 7.5 \) square units.
   - Ratio of areas \( \frac{30}{7.5} = 4 \). Thus, Triangle F is 4 times larger than Triangle G.

3. **Triangle H**:
   - Area = \( \frac{1}{2} \times 1.5 \times 2.5 = 1.875 \) square units.
   - Ratio of areas \( \frac{7.5}{1.875} = 4 \). Thus, Triangle G is 4 times larger than Triangle H.
   - Also, comparing Triangle F and Triangle H: \( \frac{30}{1.875} = 16 \). Triangle F is 16 times larger than Triangle H.

### Answers to the Questions:
1. **Triangle G and Triangle F:** Triangle F is 4 times larger.
2. **Triangle H and Triangle G:** Triangle G is 4 times larger.
3. **Triangle B and Triangle F:** (Need to solve if details were available for Triangle B).
4. **Triangle F and Triangle H:** Triangle F is 16 times larger.
5. **Triangle G and Triangle H:** Triangle G is 4 times larger.

Would you like more details or have any questions?

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### Related Questions:
1. How do you find the ratio of areas for two similar triangles?
2. What is the relationship between the side length ratio and area ratio in similar triangles?
3. How would the area ratio change if the base of Triangle G was doubled?
4. What happens to the area of a triangle if both the base and height are doubled?
5. Can you apply this knowledge to find the area of irregular shapes?

**Tip:** When dealing with similar shapes, always remember that the area scales with the square of the scale factor between corresponding sides.

For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first?

Learn how to determine how many times larger the area of one similar triangle is compared to another. This problem involves calculating the area ratios of similar triangles using the similarity theorem and area formulas. Suitable for students in Grades 8-10.

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