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The question asks to find the value of \( x \) in each right triangle using Pythagorean triples. The Pythagorean theorem states that in a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse (the longest side) and \( a \) and \( b \) are the other two sides.

Let’s go through each problem:

### 7. Triangle with sides \( x \), \( 8 \), and \( 17 \)
This is a known Pythagorean triple: \( 8, 15, 17 \). So, \( x = 15 \).

### 8. Triangle with sides \( x \), \( 24 \), and \( 45 \)
This triangle has a multiple of the triple \( 9, 12, 15 \), scaled by a factor of 3: \( 24, 45, x \). The missing side \( x = 36 \).

### 9. Triangle with sides \( x \), \( 28 \), and \( 96 \)
This is a scaled version of the triple \( 7, 24, 25 \), scaled by a factor of 4: \( 28, 96, x \). The missing side \( x = 100 \).

### 10. Triangle with sides \( 5 \), \( 12 \), and \( x \)
This is the classic Pythagorean triple \( 5, 12, 13 \), so \( x = 13 \).

### 11. Triangle with sides \( 8 \), \( 10 \), and \( x \)
This is a multiple of the triple \( 3, 4, 5 \), scaled by a factor of 2: \( 6, 8, 10 \). Therefore, \( x = 6 \).

### 12. Triangle with sides \( 12 \), \( 20 \), and \( x \)
This is a multiple of the triple \( 3, 4, 5 \), scaled by a factor of 4: \( 12, 20, x \). So, \( x = 16 \).

If you'd like further explanation for any of these, feel free to ask!

Here are 5 questions you can explore based on this:
1. How do you identify common Pythagorean triples?
2. What is the general form of a Pythagorean triple?
3. Can Pythagorean triples be applied to non-right triangles?
4. What is the difference between primitive and non-primitive Pythagorean triples?
5. How do you scale a Pythagorean triple to solve larger triangle problems?

**Tip:** Memorizing common Pythagorean triples (like \( 3, 4, 5 \) or \( 5, 12, 13 \)) can greatly speed up solving right triangle problems.

Use a Pythagorean triple to find the value of x in right triangles.

Learn how to solve for x in right triangles using Pythagorean triples. This lesson covers common triples such as (3, 4, 5) and (5, 12, 13), and includes scaled multiples of these triples. Suitable for students in Grades 8-10.

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