We are tasked with finding the value of $x$ in the given right triangle.

Step-by-Step Solution:

We are given:

• One leg of the triangle: $x$ (unknown),
• The other leg: $4$,
• The hypotenuse: $5$.

Since this is a right triangle, we can use the Pythagorean Theorem: $a^2 + b^2 = c^2$ Where:

• $a$ and $b$ are the legs,
• $c$ is the hypotenuse.

Substitute the known values: $x^2 + 4^2 = 5^2$

1. Simplify the squares: $x^2 + 16 = 25$

2. Solve for $x^2$ by subtracting 16 from both sides: $x^2 = 25 - 16$ $x^2 = 9$

3. Take the square root of both sides: $x = \sqrt{9}$ $x = 3$

Final Answer:

The value of $x$ is $3$.

The correct option is: C) $x = 3$.

Do you want further explanations on the Pythagorean theorem or any other steps? Let me know!

Here are 5 related questions you can explore:

1. What is the Pythagorean theorem, and how is it derived?
2. How do you determine if a triangle is a right triangle using its side lengths?
3. If two sides of a right triangle are given, how do you find the third?
4. How does the Pythagorean theorem apply to real-world problems?
5. What are Pythagorean triples, and can you identify examples?

Tip: In a right triangle, always remember the hypotenuse is the longest side and opposite the right angle!