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To solve for the side length \( x \) in this right triangle, we can use the **Pythagorean theorem**. This theorem states that in a right triangle:

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

where \( c \) is the hypotenuse (the longest side) and \( a \) and \( b \) are the other two sides. In this case:

- The hypotenuse \( c = 5 \)
- One leg \( b = 4 \)
- We need to find the other leg \( a = x \)

### Step-by-Step Solution
1. Substitute the values into the formula:

   \[
   x^2 + 4^2 = 5^2
   \]

2. Simplify the squares:

   \[
   x^2 + 16 = 25
   \]

3. Isolate \( x^2 \) by subtracting 16 from both sides:

   \[
   x^2 = 9
   \]

4. Take the square root of both sides:

   \[
   x = \sqrt{9} = 3
   \]

### Answer
The length of \( x \) is **3.00**, when rounded to the nearest hundredth.

Would you like further details or have any questions?

### Related Questions
1. How do you solve for the hypotenuse when given both legs?
2. What is the Pythagorean theorem and why does it work?
3. How can you verify if a triangle is a right triangle using side lengths?
4. What are the possible values of \( x \) if the hypotenuse length changes?
5. How can the Pythagorean theorem be applied in real-world scenarios?

### Tip
Remember, the Pythagorean theorem only applies to right triangles, where one angle is exactly 90 degrees.

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Learn how to find the missing side length in a right triangle by applying the Pythagorean theorem. This guide provides a step-by-step solution, ideal for students in Grade 8, using the formula a^2 + b^2 = c^2.

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