https://file.aiquickdraw.com/mathbot/file/1726780433824mibon9p7.jpg

From the image, I can see that the problem involves a right triangle. You are given the dimensions of some sides of the triangle:

- \( a = 15.99 \, \text{cm} \)
- \( b = 21.99 \, \text{cm} \)
- \( c = 14.54 \, \text{cm} \)

The goal is to determine the length of side \( x \), which seems to represent the hypotenuse of the larger triangle, made up of two smaller right triangles.

### Step-by-Step Approach:
1. The two triangles share a common height, which is represented by \( c \), and both have one side on the base line of the larger triangle.
2. Using the Pythagorean theorem on the larger triangle:
   \[
   x^2 = a^2 + (b + c)^2
   \]
   Here, the base of the larger triangle is the sum of sides \( b \) and \( c \), and \( x \) is the hypotenuse.

Let me calculate the length of side \( x \) for you.The length of side \( x \) is approximately \( 39.88 \, \text{cm} \) when rounded to two decimal places.

Would you like further details or clarification on the solution? 

Here are five follow-up questions related to this problem:
1. How would the result change if the values of \( a \), \( b \), or \( c \) were slightly different?
2. What if the triangle was not a right triangle—how would the approach differ?
3. How is the Pythagorean theorem applied to composite triangles like this one?
4. Can you verify the result by manually recalculating with different methods?
5. What other methods can you use to calculate unknown sides in triangles, besides the Pythagorean theorem?

**Tip:** Always ensure that the triangle is a right triangle before applying the Pythagorean theorem, as it only works for such triangles.

In the triangle shown above, we have a = 15.99 cm, b = 21.99 cm, and c = 14.54 cm. How long is the side x? Give your answer with TWO (2) decimal places!

Learn how to calculate the hypotenuse (x) of a right triangle with side lengths a = 15.99 cm, b = 21.99 cm, and c = 14.54 cm using the Pythagorean theorem. Suitable for high school students studying geometry.

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