https://file.aiquickdraw.com/mathbot/file/1726542135617x5hjl2uc.jpg

The image you provided contains four different triangles, with given side lengths, and the question seems to be asking you to determine certain unknown side lengths using the properties of triangles.

Since it looks like a geometric problem, I assume the context involves using the Pythagorean theorem or trigonometric principles, especially for right-angled triangles. Let's break them down one by one:

1. **Triangle a):**
   - The triangle is a right-angled triangle.
   - Given sides: 20, 21 (likely the legs).
   - We need to find the third side (hypotenuse), using the Pythagorean theorem:  
     \[
     c^2 = a^2 + b^2
     \]

2. **Triangle b):**
   - The triangle is also a right-angled triangle.
   - Given sides: 9 and 12 (legs), find the hypotenuse using the same formula.

3. **Triangle c):**
   - The sides given are 14, 24 (perhaps a non-right triangle). We might need to use other trigonometric rules or special triangle properties depending on the information provided.

4. **Triangle d):**
   - The triangle has sides 7 and 25, and one angle is marked as a right angle, so we apply the Pythagorean theorem here as well.

Do you want me to go ahead and solve these step by step using the Pythagorean theorem and relevant rules?

Determine the unknown sides of the given triangles using the properties of triangles, such as the Pythagorean theorem.

Learn how to find the unknown sides of triangles using the Pythagorean theorem. This problem involves right-angled triangles with given side lengths, such as 20, 21, and other values. Ideal for students in Grades 7-10.

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