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The image is about solving problems related to the Pythagorean Theorem, specifically for finding the hypotenuse of right-angled triangles. To apply the Pythagorean theorem, we use the formula:

\[
a^2 + b^2 = c^2
\]

Where:
- \(a\) and \(b\) are the lengths of the legs of the triangle,
- \(c\) is the length of the hypotenuse (the side opposite the right angle).

Looking at the triangles provided in the image, I will solve for the hypotenuse for the first few triangles as an example:

1. **First triangle (12 cm, 21 cm):**
   \[
   c^2 = 12^2 + 21^2 = 144 + 441 = 585
   \]
   \[
   c = \sqrt{585} \approx 24.19 \, \text{cm}
   \]

2. **Second triangle (9 cm, 11 cm):**
   \[
   c^2 = 9^2 + 11^2 = 81 + 121 = 202
   \]
   \[
   c = \sqrt{202} \approx 14.21 \, \text{cm}
   \]

3. **Third triangle (22 cm, 8 cm):**
   \[
   c^2 = 22^2 + 8^2 = 484 + 64 = 548
   \]
   \[
   c = \sqrt{548} \approx 23.41 \, \text{cm}
   \]

4. **Fourth triangle (23 cm, 16 cm):**
   \[
   c^2 = 23^2 + 16^2 = 529 + 256 = 785
   \]
   \[
   c = \sqrt{785} \approx 28.02 \, \text{cm}
   \]

5. **Fifth triangle (5 cm, 9 cm):**
   \[
   c^2 = 5^2 + 9^2 = 25 + 81 = 106
   \]
   \[
   c = \sqrt{106} \approx 10.30 \, \text{cm}
   \]

Would you like me to solve more triangles or go into more detail on how these calculations are done?

### Related Questions:
1. What is the importance of the Pythagorean Theorem in geometry?
2. Can the Pythagorean Theorem be applied to non-right triangles?
3. How can we calculate the missing side of a triangle if the hypotenuse and one leg are given?
4. How can the Pythagorean Theorem be used in real-life applications?
5. What happens if the square of the hypotenuse doesn't perfectly match a whole number?

### Tip:
Always make sure the triangle is a right-angled triangle before using the Pythagorean Theorem!

Solve for the hypotenuse in various right-angled triangles using the Pythagorean Theorem.

This page covers how to solve for the hypotenuse in right-angled triangles using the Pythagorean Theorem. Example problems include calculating the hypotenuse for various triangles, such as ones with side lengths of 12 cm and 21 cm or 9 cm and 11 cm. Suitable for Grades 7-9 geometry students.

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