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!