https://file.aiquickdraw.com/mathbot/file/1726649178841wqb6cly7.jpg

The image you provided shows a right triangle inside a quarter circle. Let's analyze it step by step to solve for \( x \).

1. **Dimensions**: 
   - The quarter circle has radius 5 (from the total vertical height, 4 + 1).
   - The base from \( O \) to \( B \) is divided into two parts: \( OB = 3 + 2 = 5 \).
   - The pink line \( x \) is the hypotenuse of the right triangle with legs 3 and 4.

2. **Using Pythagoras Theorem**:
   In a right triangle, the relation between the legs and the hypotenuse is given by:
   \[
   x^2 = \text{leg}_1^2 + \text{leg}_2^2
   \]
   Here, the legs are 3 and 4.

\[
x^2 = 3^2 + 4^2
\]
\[
x^2 = 9 + 16 = 25
\]
\[
x = \sqrt{25} = 5
\]

Thus, \( x = 5 \).

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the length of the diagonal in a right triangle with legs 5 and 12?
2. How would you calculate the area of a quarter circle with radius 5?
3. If the radius of the quarter circle was doubled, how would the value of \( x \) change?
4. What would the perimeter of the triangle in the image be?
5. How would you calculate the area of the triangle formed in the image?

**Tip**: Always apply the Pythagorean Theorem to right triangles to find missing sides when two sides are known.

Solve for x in the right triangle inside a quarter circle.

Learn how to solve for x in a right triangle inside a quarter circle with radius 5, using the Pythagorean theorem. The problem involves a triangle with legs 3 and 4, and requires calculating the hypotenuse. Suitable for students in Grades 7-9.

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