You have provided an image of a right triangle, asking to find the length of $x$. Based on the image, the triangle shows a total horizontal length of 20 feet (14.5 ft + 5.5 ft) and a vertical height of 3.44 feet.

To find $x$, we can use the Pythagorean theorem, which states:

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

where $a$ and $b$ are the legs of the right triangle, and $c$ is the hypotenuse. Given the measurements:

• One leg $a = 5.5$ ft (the smaller horizontal segment)
• The other leg $b = 3.44$ ft (the vertical segment)

Let's calculate $x$ (the hypotenuse):

$x = \sqrt{a^2 + b^2}$

Substituting the values:

$x = \sqrt{(5.5)^2 + (3.44)^2}$

Let's calculate this.The length of $x$ is approximately $6.49$ feet.

Would you like any more details or have any other questions? Here are some further topics we could explore:

1. How changing the dimensions of the triangle affects the length of $x$.
2. Explanation of how the Pythagorean theorem is derived and its historical significance.
3. Similar problems involving right triangles and the use of the Pythagorean theorem.
4. How to check if a triangle is a right triangle given its side lengths.
5. Applying this problem to real-world scenarios, such as construction or navigation.

Tip: Always ensure the triangle is a right triangle before applying the Pythagorean theorem, as it only holds true under that condition.