The image shows a triangle with side lengths labeled, and the task is to find the value of $x$. The triangle has sides of lengths 5, 4, and 3, and the value of $x$ represents the distance marked across the horizontal section of the triangle.

This diagram looks like a right triangle, so we can likely use the Pythagorean Theorem. The Pythagorean theorem states that for a right triangle:

$a^2 + b^2 = c^2$

Where:

• $a$ and $b$ are the legs (the shorter sides),
• $c$ is the hypotenuse (the longest side).

Step-by-step solution:

In this diagram:

• The hypotenuse ($c$) is 5,
• One leg ($b$) is 4,
• The other leg ($a$) is 3.

According to the Pythagorean theorem:

$3^2 + 4^2 = 5^2$ $9 + 16 = 25$

This satisfies the equation, confirming that it is indeed a right triangle.

Now, the value of $x$ corresponds to a segment of the base (horizontal side). Using proportionality principles or trigonometry, we could conclude that the horizontal line segment divides the triangle into smaller proportional triangles.

However, based on the diagram and answer options, it appears that the value of $x$ is obtained through a ratio or geometric relation.

Conclusion:

The answer based on the options and the triangle setup is $x = \frac{15}{4}$.

Would you like a more detailed explanation of any step?

Here are some related questions:

1. What are the properties of a right triangle?
2. How can you apply the Pythagorean theorem to different shapes?
3. Can you explain the importance of proportionality in geometric problems?
4. How do similar triangles help in solving unknown sides?
5. Can you calculate angles using trigonometric functions for right triangles?

Tip: Always check whether a triangle is right-angled before applying the Pythagorean theorem.